Asian share markets firmed on Monday as the Nikkei reached another new high and investors braced for a week packed with central bank events and major data that will refine market wagers for when interest rates will start falling.

Oil prices rose on Monday after OPEC+ members agreed to extend voluntary oil output cuts of 2.2 million barrels per day into the second quarter, largely in line with market expectations.

The U.S. dollar drifted weaker on Monday, pressured by lower Treasury yields, as traders waited for more crucial economic data for fresh clues on the timing of Federal Reserve interest rate cuts.

The dollar was steady on Friday after data showed U.S. inflation remained sticky but is easing gradually, keeping hopes alive that the Federal Reserve will start cutting interest rates in June, while the yen stumbled back to the key 150 per dollar level.

China's manufacturing activity in February shrank for a fifth straight month, an official survey showed on Friday, raising pressure on Beijing to roll out more stimulus measures as the parliament prepares for a key annual meeting next week.

Oil prices edged up on Friday and were set to end the week modestly higher as markets awaited an OPEC+ decision on supply agreements for the second quarter amid differing demand indicators for key consumers U.S. and China.