* Trump refused on Friday to certify Iran nuclear deal compliance
* Congress has 60 days to decide further action
* Iraq forces move towards oil-rich, Kurdish held Kirkuk
* In U.S., drillers cut back rigs searching for oil (Adds Iraq conflict, comment, graphic; updates prices)
SINGAPORE, Oct 16 (Reuters) - Oil markets jumped on Monday on concerns over potential renewed U.S. sanctions against Iran as well as conflict in Iraq, while a falling U.S. rig count supported prices there.
Brent crude futures, the international benchmark for oil prices, were at $57.82 at 0156 GMT, up 65 cents, or 1.1 percent, from the previous close.
Traders said that worries over renewed U.S. sanctions against Iran were pushing prices up.
U.S. President Donald Trump struck a blow against the 2015 Iran nuclear deal on Friday, defying both U.S. allies and adversaries by refusing to formally certify that Tehran is complying with the accord even though international inspectors say it is.
Under U.S. law, the president must certify every 90 days to Congress that Iran is complying with the deal. The U.S. Congress will now have 60 days to decide whether to reimpose economic sanctions on Tehran that were lifted under the pact.
During the previous round of sanctions against Iran, some 1 million barrels per day (bpd) of crude oil supplies were cut off global markets. While analysts said they did not expect renewed sanctions to have such a big impact again, especially as the United States would likely act alone, they did warn that such a move would be disruptive.
"If Iran (were) found breaching their nuclear agreement and had their trade agreement revoked, (that) would be the biggest catalyst for upward momentum on crude prices," said Shane Chanel, equities and derivatives adviser at ASR Wealth Advisers.
There were also concerns about the stability of Iraq, the second biggest oil producer within the Organization of the Petroleum Exporting Countries (OPEC) behind Saudi Arabia.
Iraqi forces on Sunday began moving towards oil fields and an important air base held by Kurdish forces near the oil-rich city of Kirkuk, Iraqi and Kurdish officials said.
Greg McKenna, chief market strategist at futures brokerage AxiTrader said that "Trump's reopening of the Iran nuclear issue, (and) the ongoing threat of the Kurdish pipeline being cut off" were the main factors pushing up oil prices.
U.S. RIG COUNT DROPS
Within the United States, crude prices were also up as drillers cut back the number of rigs tapping new production.
U.S. West Texas Intermediate (WTI) crude futures were trading at $51.86 per barrel, up 41 cents, or 0.8 percent.
Drillers cut five oil rigs in the week to Oct. 13, bringing the total count up to 743, the lowest since early June, General Electric Co's Baker Hughes energy services firm said in its closely followed report late on Friday. <RIG-OL-USA-BHI>
(Reporting by Henning Gloystein; Editing by Joseph Radford and Sonali Paul)