* Iran says it will enrich uranium at higher level
* "Be careful," Trump tells Tehran
* Employers added more jobs than expected last month (Updates prices, adds Brent positions)
LONDON, July 8 (Reuters) - Oil prices firmed on Monday amid tensions over Iran's nuclear program but gains were tempered by concerns about global economic growth and consequently oil demand.
Brent crude futures were up 66 cents by 1353 GMT at $64.89 a barrel. U.S. West Texas Intermediate (WTI) was up 60 cents at $58.11.
Iran on Monday threatened to restart deactivated centrifuges and step up its enrichment of uranium to 20% in a move that further threatens the 2015 nuclear agreement that Washington abandoned last year.
Washington has imposed sanctions that eliminate benefits Iran was meant to receive in return for agreeing to curbs on its nuclear program under the 2015 deal with world powers. The confrontation has brought the United States and Iran close to conflict, with U.S. President Donald Trump calling off air strikes last month minutes before impact.
On Sunday Trump issued another warning over Iran's nuclear activities. "They'd better be careful," he said.
However, oil prices continue to be pressured by lingering fears over demand.
"That the market reacts so little to the tense situation in the Middle East is a reflection of a very well-supplied market in general and a very relaxed market," said SEB chief commodities analyst Bjarne Schieldrop.
The U.S.-China trade war has dampened prospects for global economic growth and oil demand.
However, lack of concrete progress in resolving an acrimonious trade war between the United States and China means the bar could be very high for the U.S. Federal Reserve not to lower borrowing costs at its July 30-31 policy meeting.
Elsewhere, Japan's core machinery orders fell for the first time in four months in May, posting the biggest monthly drop in eight months in a worrying sign that global trade tensions are taking a toll on corporate investment.
"Concern for global growth is at the back of the mind of the whole market all the time these days," SEB's Schieldrop said.
In a sign of growing concern over the health of the global economy and its impact on oil demand, investors cut their ICE Brent net long positions by 6,748 contracts to 248,006 in the week to July 2.
Strong U.S. economic data also put a floor under prices. U.S. job growth rebounded strongly in June, with government payrolls surging, a closely watched employment report showed on Friday, suggesting that May's sharp slowdown in hiring was probably a one-off.
The owner of Britain's biggest oil pipeline, Ineos, on Sunday said it had started to reduce flows on the Forties pipeline system to repair a processing unit at Scotland's Kinneil plant. On Monday it said that flows had fallen to about 180,000 barrels per day (bpd) and that it expects the unit to be back online by Friday.
The pipeline system typically pumps about 450,000 bpd.
(Additional reporting by Aaron Sheldrick in TOKYO Editing by Kirsten Donovan and David Goodman)