* EU works on second bailout package for Greece
* Canada-U.S. crude pipeline shut by leak, lifts crude
* Coming up: API oil inventory data, 4:30 p.m. EDT Tuesday
(Recasts, updates market activity, prices to settlement)
By Robert Gibbons
NEW YORK, May 31 (Reuters) - Oil prices rose 2 percent on Tuesday, lifted by the closure of a pipeline carrying Canadian crude to the United States and a decline in the dollar on new hopes for a debt bailout for Greece.
Both Brent and U.S. crude prices reached three-week highs intraday, but still posted monthly declines for May that were the biggest in a year in percentage terms.
TransCanada Corp
"In case of a longer disruption, we might see a noticeable crude stock draw in Cushing in next week's US inventory reports," said JBC Energy in a note.
Adding to the crude supply problems, storm-related power
outages shut down a number of Enbridge Inc's
Brent crude for July delivery
Brent posted a 7.3 percent loss in May, its biggest monthly percentage loss since May 2010.
U.S. July crude
U.S. crude lost 9.9 percent in May, also its biggest monthly percentage loss since May 2010. Both Brent and U.S. crude contracts have been rebounding from a commodities sell-off earlier in May.
Brent and U.S. crude oil trading volumes were on pace on Tuesday to end the day below 30-day averages.
The euro
U.S. June gasoline
Oil's gains came despite disappointing reports showing falling U.S. home prices, a drop in U.S. consumer confidence in May and much slower growth than expected in the U.S. Midwest. [ID:nN31289567]
The less-than-steller data came ahead of Friday's closely watched U.S. May non-farm payrolls report.
Oil prices also received a lift from the end of a truce between tribal groups and forces loyal to Yemen's President Ali Abdullah Saleh. [ID:nLDE74U00R]
Street fighting raged across the Yemeni capital after the breakdown of the truce, edging the Arab country that borders Saudi Arabia closer to civil war.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
For timeline on Yemen troubles [ID:nLDE74H12F]
For an analysis on al Qaeda in Yemen [ID:nLDE74Q08P]
For more on Yemen unrest [ID:nLDE73R1DP]
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^>
South African President Jacob Zuma made little headway toward brokering a Libya peace deal in talks with Muammar Gaddafi, who is adamant he will not leave Libya. [nJ8E7EP02X]
"The dollar and the geopolitical concerns had crude up, but the (Midwest business activity) and consumer confidence data took away some of the momentum," said Phil Flynn, analyst at PFGBest Research in Chicago, commenting on oil's choppy trajectory.
The developments in Yemen and the conflict in Libya will keep the turmoil in North Africa and the Middle East in focus as OPEC oil ministers gather in Vienna in early June.
U.S. OIL INVENTORIES
Weekly U.S. oil inventory data from industry and government are delayed this week after the Monday's U.S. Memorial Day.
A Reuters poll of analysts on Tuesday yielded a forecast for crude stockpiles to have fallen last week, with gasoline stocks higher and distillate stocks up slightly. [EIA/S]
The industry group American Petroleum Institute will release its weekly report at 4:30 p.m. EDT (2030 GMT) on Wednesday. (Additional reporting by Claire Milhench in London and Seng Li Peng in Singapore; Editing by Alden Bentley, Sofina Mirza-Reid and David Gregorio)