Traders said the higher prices in front-month crude futures were due to expectations of a tighter market.
The Organization of the Petroleum Exporting Countries (OPEC) and other producers led by Russia have announced cutbacks of almost 1.8 million barrels per day (bpd) in oil production from January 2017 in an effort to bolster prices to reduce rampant global overproduction which has seen output outstrip consumption for over two years.
"With investors now expecting a relatively high level of compliance with the production cut agreements, prices should be well supported," ANZ bank said on Monday.
"Saudi Arabia has stated its willingness to cut production below 10 million bpd if needed (down from around 10.5 million bpd currently), which should limit risk to the deal," U.S. bank Morgan Stanley said on Monday, adding that some of the non-compliance risk to the deal to cut output in 2017 came from Iraq, which increased its January loadings versus December.
ANZ bank said that "some weakness in U.S. dollar also helped improve (oil) investor sentiment."
The dollar has lost 0.8 percent against a basket of other leading currencies since hitting 2002 highs last week.
Swings in the dollar can affect oil demand as they influence fuel prices for any country using its own currency domestically.
Despite this, there were factors that weighed on markets, preventing prices - which remain relatively low - from rising more.
In the United States, which did not participate in the production cut deal, drilling for new oil has increased for seven weeks.
Drillers added 12 oil rigs in the week to Dec. 16, bringing the total to 510, the highest since January, though still below 541 rigs a year ago, energy services firm Baker Hughes said on Friday.
"Since its trough on May 27, 2016, producers have added 194 oil rigs (+61 percent) in the U.S.," U.S. bank Goldman Sachs said.
As a result, US oil production is edging up, rising from below 8.5 million bpd in July to almost 8.8 million bpd by mid-December.