Asian shares bounced and the safe-haven dollar edged lower on Tuesday as investors hoped this week's U.S. inflation data supports an imminent end to rate hikes and cheered the prospect China will deliver economic stimulus to prop up stalling growth.

Oil prices edged higher on Tuesday, recouping some of the losses from the previous session, as traders focused on supply cuts by the world's biggest oil exporters Saudi Arabia and Russia and a weaker dollar.

The dollar weakened on Tuesday after Federal Reserve officials signalled that the central bank was nearing the end of its tightening cycle, though it traded in a tight range ahead of a key U.S. inflation report.

U.S. Treasury Secretary Janet Yellen called on Friday for market reforms in China and criticized its recent tough actions against U.S. companies and mineral export controls, while China's premier called on her to "meet China halfway" and put bilateral relations back on track.

The United States is seeking a healthy competition with China based on fair rules that benefit both countries, not a "winner-take-all" approach, U.S. Treasury Secretary Janet Yellen told Chinese Premier Li Qiang in a meeting in Beijing on Friday.

U.S. Treasury Secretary Janet Yellen on Saturday urged closer communication between China and the United States to improve economic decision-making, and challenged China to join global initiatives to help poorer nations address climate change.