Brent prices have gained almost 6 percent this month, buoyed by expectations the United States will renew sanctions.
The oil price rallied after Israeli Prime Minister, Benjamin Netanyahu, accused Iran of lying "big time" about a secretive nuclear weapons programme, ratcheting up tensions in a region that controls nearly half the world's oil.
Trump has until May 12 to decide whether to restore sanctions on Iran that were lifted after the worldwide agreement.
"The dollar has held crude back from gaining further ground".
President Trump has until May 12 to make a decision about Iran. The more-active July contract traded at US$73.16.
Oil prices rose on Monday after Israeli Prime Minister Benjamin Netanyahu stepped up pressure on the United States to pull out of the 2015 nuclear deal with Iran, presenting what he called evidence of a secret Iranian nuclear weapons programme.
The risk of the USA pulling out of the Iran nuclear deal, resulting in sanctions on the producing nation, has already largely been priced in, underpinning the market, he said.
"I doubt we will see a big sell off before we have some clarity on the Iran nuclear deal", said Torbjorn Kjus, senior oil analyst at DnB markets in Oslo.
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A rise in United States government borrowing costs to their highest since 2013 this week, has tempered some investor appetite for risk, but analysts said Brent crude futures, the global benchmark, may yet rise toward new 2018 peaks above $75 a barrel.
In the U.S., working oil rigs rose by five last week to 825, the highest level since March 2015, according to data from Baker Hughes. The global benchmark crude traded at a US$6.43 premium to June WTI.
OPEC and its partners agreed to cut oil output by 1.8 million barrels per day since January past year, an effort which has recorded a 149 percent success, and has boosted prices to $74 per barrel as at Thursday.
"There are worries that Iran's oil exports could fall by about 1 million barrels per day from current levels", said Tomomichi Akuta, senior economist at Mitsubishi UFJ Research and Consulting in Tokyo.
But while US producers are accelerating shale drilling in areas in the United States, higher production has not necessarily translated into stronger refining results for some oil companies. US crude stockpiles probably increased by 1.25 million barrels, according to the median estimate of analysts surveyed by Bloomberg.
USA crude's discount to Brent hit its widest since December 28 at $6.74 a barrel.
Additionally, U.S. crude production has soared more than 25 percent since mid-2016 to a record 10.59 million barrels per day (bpd). At the same time, OPEC's production cuts have continued to tighten global markets, despite US crude output hitting fresh records and the number of rigs reaching the highest levels since 2015.