NEW YORK (Reuters) - Crude futures surged for a second day on Friday, with both U.S. and Brent contracts posting their largest weekly percentage gains on record due to hopes that a global deal to cut crude supply worldwide will emerge early next week.

On Thursday, oil staged its largest one-day rally in history on prospects for a cut in supply equivalent to anywhere from 10% to 15% of world demand. The sharp rebound from weeks of losses came after U.S. President Donald Trump said Russia and Saudi Arabia will negotiate to end a price war that slashed prices last month by more than half. Trump said the United States has not agreed to cut its output.

The rally continued Friday, with Brent crude LCOc1 futures jumping 13.9%, or $4.17 a barrel to settle at $34.11. Brent soared as much as 47% on Thursday for its highest intraday percentage gain on record, closing up 21%. The contract ended the week 36.8% higher, the largest weekly percentage gain in the contract's history.

U.S. West Texas Intermediate (WTI) crude CLc1 rose $3.02, or 11.93% to settle at $28.34 a barrel. The contract posted a 31.8% gain on the week, also its largest on record.

OPEC has scheduled a Monday emergency meeting, led by Saudi Arabia, where cuts equal to 10% of world supply - about 10 million barrels per day - could be agreed-upon.

“Grand oil bargain diplomacy clearly shifted into high gear overnight and cuts are likelier than they were until yesterday,” said Robert McNally, president of Rapidan Energy Group in Bethesda, Maryland. “The size of cuts seems to be increasing, and the timing is accelerated.”

Moscow and Washington still have made no firm commitments on output cuts. On Friday, Trump and Russian President Vladimir Putin were to meet separately with top producers. U.S. law forbids producers from cooperating to cut output.

Even a monumental cut in world output would not reduce a glut by much due to slumping demand during the worsening coronavirus pandemic, which has already sickened more than a million people worldwide.

The head of the International Energy Agency, Fatih Birol, said that even if OPEC+ cut supply by 10 million bpd, global oil stocks would build by 15 million bpd in the second quarter.

Trump said on Thursday he had spoken with both Putin and Saudi Crown Prince Mohammed bin Salman and they had agreed to reduce supplies by 10 million to 15 million barrels per day (bpd) out of total global supply of about 100 million bpd.

“It does appear that momentum is growing for some form of output agreement,” said analyst Harlan Matthews at Redburn Energy.

“(But) there are huge obstacles to any output agreement on this scale, and even if it were to be implemented the market would remain chronically oversupplied in the near term.”

The Canadian province of Alberta, home to the world’s third-largest oil reserves, is open to joining any potential global pact to reduce a glut of crude.

Mexico does not plan to cut crude production at state-owned oil company Pemex, even at its most expensive oilfields, amid a severe decline in global prices, the country’s energy minister Rocio Nahle told Reuters on Friday.

By cutting output by 10 million bpd, “the oil industry would get at least three weeks more room to prepare for hitting the wall when there are no more places to put the excess production,” said Rystad Energy’s Per Magnus Nysveen.

Trump is meeting with oil company executives at the White House on Friday afternoon to discuss a historic oil-price slump threatening their businesses, brought on by the coronavirus outbreak and a Saudi-Russia price war.