FORM 6-K

                             WASHINGTON, D.C. 20549

                        Report of Foreign Private Issuer
                        Pursuant to Rule 13a-16 or 15d-16
                     of the Securities Exchange Act of 1934

For May 18, 2004

                        International Uranium Corporation
                 (Translation of registrant's name into English)

                 Independence Plaza, Suite 950, 1050 Seventeenth
                            Street, Denver, CO 80265
                    (Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports
under cover Form 20-F or Form 40-F.

               Form 20-F [X]                       Form 40-F [ ]

Indicate by check mark whether the registrant by furnishing the information
contained in this Form is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                   Yes [ ]                            No [X]

If "Yes" is marked, indicate below the file number assigned to the registrant in
connection with Rule 12g3-2(b): 82- ________________.



Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                                             International Uranium Corporation

Date:  June 2, 2004                          By:  /s/  Ron F. Hochstein
       ------------------                         ---------------------
                                                  Ron F. Hochstein, President

                                  EXHIBIT INDEX

Exhibit Number         Description
--------------         -----------
      1                Press Release dated May 18, 2004

CONTACT: SOPHIA SHANE        2101, 885 West Georgia Street         INTERNATIONAL
Corporate Development        Vancouver, British Columbia              URANIUM
Tel:  (604) 689-7842         Canada  V6C 3E8                        CORPORATION
Fax:  (604) 689-4250         www.intluranium.com



RESOURCES INC. ("JNR") are pleased to provide an update on the Moore Lake
uranium project located in the Athabasca Basin of northern Saskatchewan.

The Companies had a very successful winter drilling program on the Moore Lake
project. A total of 6,747 metres were completed in 19 diamond drill holes. The
results not only expanded the extent of the known high grade uranium zone but
also significantly expanded the extent of the mineralizing system associated
with the high grade Maverick zone to at least 800 metres northeast of the
discovery hole, ML-25. Please see the attached map which shows the intense
alteration and mineralization halo associated with the northeast trending
conductive structural corridor. The second attached map shows the numerous
additional conductors on trend within the Moore Lake property (map available
from the Company or www.intluranium.com).

The first 8 holes (ML-28 to ML-35) of the 2004 winter program focused primarily
on the high grade Maverick zone and returned two new high grade uranium
intercepts in Holes ML-29 and ML-35.

Hole ML-29, based on probe results, returned a grade equivalent of 1.3% U3O8
over 7.5 metres (261.5 to 269.0 m), including 2.3 metres of 3.6% U3O8. Within
the higher grade core there was one continuous 0.5 metre sample that assayed
7.91% U3O8, as well as 3.65% nickel, 1.6% copper, 0.9% cobalt, 0.7% zinc, 0.35%
total rare earths and 5 g/t silver. The presence of high levels of these
"pathfinder" elements is significant in that this association is unique and
common to the larger unconformity uranium deposits in the Athabasca Basin.

Hole ML-35 intersected 11.1 metres of uranium mineralization (262.4 to 273.5 m).
The upper 4.9 metres was low-grade sandstone-hosted mineralization that assayed
0.05% U3O8. Immediately beneath that was a 0.7 metre section of lost core,
followed by 5.5 metres that assayed 1.61% U3O8, including a 1.5 metre interval
grading 5.3% U3O8. The 0.7 metre lost core interval returned a grade equivalent
of 2.69% U3O8, based on probe results.

The next 11 holes were largely of a reconnaissance nature and focused on
identifying the extent of the mineralizing system for further follow up this
summer. Targets identified by a recently completed ground electromagnetic (EM)
survey were also tested. The geochemical results have been received for drill
holes ML-36 to ML-41 and indicate that the mineralizing system continues
northeast and southwest of the previously identified limits.

Drillholes ML-40 and ML-41 were progressive 150 metre stepouts to the northeast
of ML-34. They intersected strong alteration and structural disruption in the
basal portion of the sandstone column, accompanied by anomalous levels of
uranium and lead. More significantly, they intersected up to 65 meters of highly
altered and structurally disrupted graphitic pelites and pelites well beneath
the unconformity. Select samples from these rocks returned anomalous levels of
uranium and 'pathfinder elements' such as nickel, cobalt, lead, zinc and
vanadium. ML-40 and ML-41 were collared well into the hanging wall and will be
followed up this summer. They also indicate that the mineralizing system now
continues a minimum of 800 metres northeast of the section containing the
discovery hole (ML-25).

Drillholes ML-37 and ML-36 were progressive 50 metre stepouts to the southwest
of the mineralized section containing ML-03 and ML-29. Both holes were
structurally disrupted and altered over their entirety. The better results were
obtained from ML-37 which intersected a broad low grade zone of uranium
mineralization at the unconformity. Probe results indicate a grade equivalent of
0.11% U3O8 over 17 metres; including narrower intercepts of 0.46% U3O8 over 1.5
metres, and 0.88% U3O8 over 0.6 metres. Both holes also returned highly
anomalous values of pathfinder elements, throughout the sandstone column and the
basement pelites.

Drillholes ML-38 and ML-39 were targeted on EM and structural features
interpreted from this winter's geophysical program. ML-38 was collared some 450
metres southwest of the discovery hole. This hole intersected abundant faulting
and alteration in the upper 150 metres of the sandstone column, accompanied by
highly anomalous uranium and boron values. ML-38 also intersected strongly
altered, faulted and geochemically anomalous graphitic pelites some 40 metres
beneath the unconformity; suggesting a multiplicity of mineralized structures in
this area. This hole also indicates that the mineralizing system continues a
minimum of 450 metres southwest of the discovery hole.

ML-39 was targeted on a geophysically interpreted north-northwest trending
structure, located some 500 metres to the northwest of the discovery hole. ML-39
missed the target but did intersect a strongly altered lower sandstone column
that returned highly anomalous uranium, lead and boron values.

Samples from the remaining 5 holes drilled this winter are in the lab.

IUC and JNR are very pleased with these results which are indicative of a
potentially sizeable and high grade uranium system - the newest high grade
discovery in the rich Athabasca Basin. A second drill and supplies for an
extensive summer program were brought in over the ice before breakup, and are on
site. The summer drilling program is expected to begin in early June.

The companies have also recently staked additional ground to the northeast and
the southwest of the existing Moore Lake project, thereby increasing their land
position in the area by 60%, to almost 37,000 hectares.

Drill core was prepared and assayed by the Saskatchewan Research Council in
accordance with industry standards. Drill results and technical data have been
reviewed by Richard Kusmirski, P.Geo., a Qualified Person pursuant to NI 43-101.

Statements contained in this news release which are not historical facts are
forward-looking statements that involve risks, uncertainties and other factors
that could cause actual results to differ materially from those expressed or
implied by such forward-looking statements. Factors that could cause such
differences, without limiting the generality of the following, include:
volatility and sensitivity to market prices for uranium; the impact of the sales
volume of uranium; competition; the impact of change in foreign currency
exchange rates and interest rates; imprecision in reserve estimates;
environmental and safety risks including increased regulatory burdens;
unexpected geological or hydrological conditions; political risks arising from
operating in certain developing countries; a possible deterioration in political
support for nuclear energy; changes in government regulations and policies,
including trade laws and policies; demand for nuclear power; replacement of
production and failure to obtain necessary permits and approvals from government
authorities; weather and other natural phenomena; ability to maintain and
further improve positive labour relations; operating performance of the
facilities; success of planned development projects; and other development and
operating risks. Although IUC believes that the assumptions inherent in the
forward-looking statements are reasonable, undue reliance should not be placed
on these statements, which only apply as of the date of this report. IUC
disclaims any intention or obligation to update or revise any forward-looking
statement, whether as a result of new information, future events or otherwise.


Ron F. Hochstein

                               MOORE LAKE CLAIMS


                               MOORE LAKE PROJECT
                             MAVERICK AREA DRILLING