Brent crude futures gained 28 cents, or 0.4%, to USD 79.90 a barrel by 0427 GMT and U.S. West Texas Intermediate crude futures was up 0.3%, or 26 cents, at USD 75.79 a barrel.
On Friday, data showed the U.S. added more jobs than expected last month, leading investors to trim expectations for rate cuts, which helped the dollar to rally.
A stronger greenback makes dollar-denominated commodities such as oil more expensive for holders of other currencies.
The euro also came under pressure, reflecting uncertainty in the eurozone after French President Emmanuel Macron called snap legislative elections for later in June after he was trounced in the European Union vote by Marine Le Pen's far-right party.
"Regarding Macron and elections, it does create another layer of uncertainty, coming after the upside surprise in U.S. non-farm payrolls, which saw yields scream higher," Tony Sycamore, a Sydney-based analyst at IG said.
Markets are now focused on the U.S. Federal Reserve and Bank of Japan meetings this week, with the risks of more hawkish outcomes, Sycamore said.
"That will likely create more angst amongst some of the member states of OPEC+ as to when they can return their cuts back to the market given the negative reception this proposal received last week post the OPEC+ meeting."
Brent and WTI posted their third straight weekly loss last week on concerns that a plan to unwind production cuts by the Organization of the Petroleum Exporting Countries and their allies, a group known as OPEC+, from October will add to rising global supply.
The announcement coincided with a rise in total commercial OECD crude and product stocks on land to an estimated 48 million barrels in May, compared with the average build of 30 million barrels during 2015-2019, energy consultancy FGE said in a note.
Analysts and traders expect summer holiday demand to reduce stockpiles and support prices.
"We continue to expect the market to firm up and crude prices to reach mid-USD 80/bbl levels as we move into 3Q 2024, but it will likely need a convincing signal of tightening from preliminary inventory data," FGE said.
Goldman Sachs analysts expect Brent to rise to USD 86 a barrel in third quarter.
"We expect that healthy consumers and solid summer demand for transportation and cooling will push the market in a sizable Q3 deficit of 1.3mb/d."
In the U.S., Washington stepped up purchasing of crude oil to replenish the Strategic Petroleum Reserve after prices fell.
Last week, U.S. energy firms cut the number of oil and natural gas rigs operating to the lowest since January 2022, energy services firm Baker Hughes said on Friday.
In the Middle East, Iraq's Oil Minister Hayan Abdel-Ghani said there has been progress in talks with Kurdistan region officials and representatives of international companies operating there for a deal to resume oil exports via the Iraq-Turkey oil pipeline that once handled about 0.5% of global oil supply.
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