By Christopher Johnson
Brent crude oil jumped by $1.89 or 3 percent to a high of $63.58 before slipping back to trade around $62.25, up 56 cents by 1425 GMT.
U.S. light crude was last up 20 cents at $53.15 after earlier gaining more than 3 percent to an intraday high of $54.55 a barrel.
Both benchmarks climbed by around 4 percent on Monday after U.S. President Donald Trump and Chinese counterpart Xi Jinping agreed at a meeting of the Group of 20 industrialised nations (G20) to pause an escalating trade dispute.
"Buying pressures remain at the fore of the energy complex as market players keenly await fresh supply curbs," said Stephen Brennock, analyst at London brokerage PVM Oil.
The Organization of the Petroleum Exporting Countries meets on Thursday in Vienna to agree output policy and will discuss its strategy with producers outside OPEC, including Russia.
OPEC and its allies are working towards a deal to reduce output by at least 1.3 million barrels per day (bpd), OPEC sources have told Reuters, adding that they were still talking to Russia about the extent of its production cuts.
However Saudi Oil Minister Khalid Al-Falih said it was too soon to be certain that OPEC and other oil exporters would cut production because the terms of a deal remain unresolved.
Al-Falih said he thought the market was oversupplied but he cautioned that all members of OPEC and its allies needed to come together for a cut to go ahead.
"A cut in OPEC and Russia production of 1.3 bpd will be required to reverse the ongoing counter-seasonally large increase in inventories," Goldman Sachs said in a note.
It added that it expected a joint effort by OPEC and Russia to withhold supply to push Brent oil prices "above the mid-$60 per barrel level".
Helping OPEC in its efforts to rein in emerging oversupply was an order on Sunday by the Canadian province of Alberta for producers to scale back output by 325,000 bpd until excess crude in storage is reduced.
OPEC's biggest problem is surging production in the United States, where output - mostly from its southern shale fields - has grown by about 2 million bpd within a year to more than 11.5 million bpd.
Barclays bank said in a note to clients that oil production in Texas alone "reached 4.69 million bpd in September, compared with Iraqi output of 4.66 million by our estimates".
Iraq is OPEC's second-biggest oil producer behind Saudi Arabia.
(Reporting by Christopher Johnson in London and Henning Gloystein in Singapore; Editing by Ed Osmond and Kirsten Donovan)
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