* WTI and Brent off five-month lows hit this week
* Trade worries linger as China-U.S. dispute intensifies
* Coming Up: U.S. rig count data at 1 p.m. EDT (New throughout, updates prices, market activity and comments; changes byline, dateline, previous LONDON)
NEW YORK, June 7 (Reuters) - Oil prices rose on Friday, climbing further from five-month lows hit this week, after Saudi Arabia said OPEC was close to agreeing to extend an output production cut beyond June.
Brent crude futures rose 91 cents, or 1.5 percent, to $62.58 a barrel by 11:09 a.m. EDT (1509 GMT). U.S. West Texas Intermediate (WTI) crude futures rose 81 cents, also 1.5 percent, to $53.40 a barrel.
Both benchmarks were on track for a third weekly decline. On Wednesday they hit their lowest since January.
Saudi Energy Minister Khalid al-Falih told a conference in Russia that the Organization of the Petroleum Exporting Countries (OPEC) and its allies should extend oil production cuts.
He said that while OPEC was close to agreement, more talks were needed with non-OPEC countries that were part of the deal to reduce output by 1.2 million barrels per day (bpd), which runs out at the end of this month.
Supply has also been limited by U.S. sanctions on oil exports from Venezuela and Iran. On Thursday, Washington tightened pressure on Venezuela's state-owned oil company by making clear that exports of diluents by international shippers could be subject to sanctions.
Investors awaited U.S. rig count data, due out at 1:00 p.m. EDT (1700 GMT). The data serves as an indication for future production.
Demand sentiment remains weak as investors worry about a stalling global economy and an intensifying trade war between the United States and China.
The United States has also threatened tariffs on goods from major trading partner Mexico. U.S. President Donald Trump vowed that tariffs of 5% will be imposed on all Mexican exports to the United States on Monday if Mexico does not step up efforts to stem an increase in migrants heading for the U.S. border.
U.S. and Mexican negotiators resumed migration talks on Friday. Marc Short, chief of staff to U.S. Vice President Mike Pence, said the administration planned to move forward with a legal notification of its planned 5% tariff.
But some market participants were skeptical the tariffs would go into effect on Monday.
"We believe that Trump will delay any tariffs as he will attempt to preclude another dive in the stock market," Jim Ritterbusch of Ritterbusch and Associates said in a note.
Because of weak economic data and the widening trade conflict, Commerzbank revised their third-quarter forecast for Brent down to $66 from $73 a barrel.
(Additional reporting by Shadia Nasralla in London and Aaron Sheldrick in Tokyo Editing by Dale Hudson and David Gregorio)