Brent crude rose $1.65, or 2.8 percent, to settle at $60.64 a barrel. US crude futures ended $1.60, or 3.2 percent, higher at $52.11 a barrel.
"Some of the fears about the economic slowdown in 2019 seem to have ebbed away," said Gene McGillian, director of market research at Tradition Energy in Stamford, Connecticut. "The market is latching on to news that suggests that the economy may be better than thought."
China's National Development and Reform Commission offered some support on Tuesday, signaling it might roll out more fiscal stimulus. This countered negative sentiment from Monday when crude prices fell more than 2 percent after data showed weakening imports and exports in China.
However, both oil benchmarks pared gains slightly in post-settlement trade after British lawmakers defeated Prime Minister Theresa May's Brexit divorce deal by a crushing margin, triggering political upheaval that could lead to a disorderly exit from the European Union or even to a reversal of the 2016 decision to leave.
Parliament voted 432-202 against her deal, raising economic uncertainty that weighed on markets.
Fundamentally, output cuts from the Organization of the Petroleum Exporting Countries and other producers, including Russia, have begun to reduce fears of oversupply.
The group, known as OPEC+, agreed in late 2018 to cut supply starting this month, seeking to rein in a global glut.
OPEC+ have set a meeting for March 17 to 18 to monitor implementation of their pact, sources told Reuters, and another meeting on April 17 to 18 to decide on whether to extend cuts beyond the agreed six months.
Further support has come from data showing the number of US rigs drilling for new oil dipped slightly so far this year. Also, analysts in a Reuters poll, ahead of weekly industry data on Tuesday and a government report on Wednesday, expected US crude stockpiles to have fallen for a second straight week.
The rig data could signal a slowing of the swift rise in output from the United States, which became the world's top oil producer in 2018.
In the longer term, US crude output is expected to rise to a new record of more than 12 million barrels per day (bpd) this year and to climb to nearly 13 million bpd next year, the US Energy Information Administration said in its first 2020 forecast.
The market also found support in news that the US will not grant further waivers to its sanctions on Iran.
US Special Representative for Iran Brian Hook said on Saturday that Washington was not looking to grant any more waivers for Iranian oil after the reimposition of US sanctions. The move could limit Iranian oil coming the market in coming months.
Such positive signals and hopes for renewed US-China talks to resolve trade tensions have boosted world stock markets and oil prices, but fears about global growth weigh heavily.
"It would seem that the market is having a rather hard time making up its mind as to which story to believe in," consultancy JBC Energy said.