* Pompeo says "significant" sanctions will be announced on Tehran
* Analysts see OPEC+ cut pact extension likely
* Russian energy minister praises cooperation
* Interactive graphic on U.S. rig count: https://tmsnrt.rs/2XdttIW (Changes dateline, updates prices, adds comment)
LONDON, June 24 (Reuters) - Oil prices rose on Monday, extending vast gains last week prompted by tensions between Iran and the United States, as Washington was set to announce new sanctions on Tehran.
Brent futures were up 11 cents, or 0.17%, at $65.31 a barrel by 0845 GMT.
West Texas Intermediate crude was up 40 cents, or 0.7%, at $57.83 a barrel.
Oil prices surged after Iran shot down a drone on Thursday that the United States claimed was in international airspace and Tehran said was over its territory.
Brent racked up a gain of about 5% last week, its first weekly gain in five weeks, and WTI jumped about 10%, its biggest weekly percentage gain since December 2016.
U.S. President Donald Trump said on Friday that he called off a military strike to retaliate for the incident, saying the potential Iranian death toll would be disproportionate, adding on Sunday that he was not seeking war.
But U.S. Secretary of State Mike Pompeo said "significant" sanctions on Iran would be announced on Monday aimed at further choking off resources that Tehran uses to fund its activities in the region.
Meanwhile, global supply may remain tight as OPEC and its allies including Russia appear likely to extend their oil cut pact at their meeting July 1-2 in Vienna, according to analysts.
"An extension of OPEC+ production cuts through the end of the year seems highly likely given recent price action", U.S. investment bank Jefferies said in a note.
"The market expects an extension though, and any failure could see oil price gap down. The probabilities favor restraint however," it added.
Russian Energy Minister Alexander Novak on Monday said international cooperation on crude production had helped stabilise oil markets and is more important than ever.
"There is a good example of successful cooperation in balancing the oil market between the OPEC countries and non-OPEC. Thanks to joint efforts, we today see a stabilisation of world oil markets," Novak said.
Boosting oil demand, prospects of a near-term interest rate cut by the Federal Reserve aimed at bolstering the U.S. economy have weakened the dollar.
Oil is usually priced in dollars, and a slide in the value of the weaker greenback makes it cheaper for holders of other currencies.
Meanwhile, Baker Hughes said on Friday that U.S. energy companies added an oil rig last week, the first increase in three weeks, bringing the total count to 789. <RIG-OL-USA-BHI>
(Additional reporting by Aaron Sheldrick; Editing by Joseph Radford and Louise Heavens)