* WTI, Brent come off five-month lows hit this week
* Trade worries linger as China-U.S. dispute intensifies
* U.S. oil production interactive: https://tmsnrt.rs/2DwTUBQ (Updates prices, adds comment, detail)
LONDON, June 7 (Reuters) - Oil prices rose on Friday, climbing further from five-month lows hit this week amid signs that OPEC and other producers may extend their output reduction deal.
Brent crude futures were up 59 cents at $62.26 a barrel by 1020 GMT. U.S. West Texas Intermediate (WTI) crude futures gained 49 cents to $53.08 per barrel.
Oil prices jumped after Saudi Energy Minister Khalid al-Falih told a conference in St Petersburg, Russia, that $60 a barrel was too low to encourage investment in the industry. Crude later pared gains.
Falih said he did not want to boost Saudi production to make up for a lower oil price and that a return to the price-crash environment of 2014-15 was unacceptable.
A deal by the Organization of the Petroleum Exporting Countries and other producers including Russia to reduce output by 1.2 million barrels per day runs out at the end of this month.
"On the OPEC side, a rollover is almost in the bag. The question is to calibrate with non-OPEC," Falih said.
"I don't think there will be a need to deepen the cut ... I'm hoping it will be an easy decision and that we'll roll over, but if it's not, we will be flexible in terms of our position."
Supply has also been limited by U.S. sanctions on oil exports from Iran and Venezuela.
However, demand sentiment remains weak amid fresh signs of a stalling global economy and an intensifying trade war between the United States and China.
The United States has also threatened to put tariffs on goods from its major trading partner Mexico.
Mexican and U.S. officials held a second day of talks on Thursday, fuelling optimism a deal could be close, although it was unclear whether Mexican pledges to curb migration were enough to persuade Washington to postpone tariffs.
"The weak economic data and widening trade conflict have made for a gloomier demand outlook. In response, we have revised our third-quarter forecast for Brent down to $66 (previously $73)," Commerzbank said in a note.
Brent is heading for a third week of declines, down more than 3%.
On Wednesday, Brent and WTI hit their lowest since mid-January at $59.45 and $50.60, respectively, after U.S. crude output <C-OUT-T-EIA> reached a record high and stockpiles climbed.
(Additional reporting by Aaron Sheldrick in TOKYO; Editing by Dale Hudson and Jason Neely)