Also speaking ahead of yesterday's scheduled ministerial panel meeting of top OPEC and non-OPEC oil producers, in Saudi Arabia, the country's Energy Minister, Khalid al-Falih, said he recommended "gently" driving oil inventories down at a time of plentiful global supplies, adding that OPEC would not make hasty decisions about output ahead of the June meeting.
The warning relayed Saturday by U.S. diplomatic posts from the Federal Aviation Administration underlined the risks the current tensions pose to a region crucial to global air travel.
At this weekend's meeting, discussion could revolve around a possible production increase after the end of the US sanction waivers to all Iranian oil buyers. "We have to be cautious", Falih said.
Oil hit multi-week highs on Monday after OPEC indicated it was likely to maintain production cuts that have helped boost prices this year, while escalating Middle East tensions provided further support.
"We have seen inventory building".
Last October, Iran's Minister of Petroleum Bijan Zangeneh said there was no spare capacity left for oil producers to pump more, dismissing Trump's pressure on OPEC to ramp up output to bring down prices.
The meeting "affirmed its commitment to achieving a balanced market and working towards oil market stability", said a statement issued at the end of the gathering.
However, it appears the members are leaning to continuing the cuts.
It came days after mysterious sabotage attacks on several tankers in highly sensitive Gulf waters and drone strikes on a Saudi crude pipeline by Yemen rebels who Riyadh claimed were acting on Iranian orders.
But Falih reiterated Sunday that the kingdom's oil installations were well protected.
USA hawks on Iran, led by National Security Adviser John Bolton, have reportedly advocated to confront Iran while Trump himself has showed restraint on further escalating the situation.
Opec+ representatives are due to meet in Vienna on June 25-26 for their next oil policy meeting.
Saudi Arabia said on Sunday that it wants to avert war in the region but stands ready to respond with "all strength" following last week's attacks on Saudi oil assets, telling Iran that the ball was now in its court.
Novak said Russian Federation would restore its output in May and that contaminated oil would not affect its annual output forecast.
The market will next watch for the U.S Energy Information Administration oil stockpiles report due on Wednesday morning.
Traders were also looking at increased Middle East tensions, which have been rising after the White House ordered warships and bombers to the Persian Gulf two weeks ago.
Both attacks targeted routes built as alternatives to the Strait of Hormuz, the conduit for nearly all Gulf exports.
He said a sabotage attack against four oil tankers off the Emirates' coast had come at a "sensitive and hard period in the region".