- Asian stocks fell after a rally in US stocks faded, with Fed officials signaling that the central bank will likely need to raise interest rates above 5% before pausing and holding for some time.

- Chinese shares in Hong Kong fell after gaining 2% on Monday, while Japan's Topix index rose after reopening after a public holiday. Australian and Southeast Asian gauges also fell. Contracts on the S&P 500 fell after the index failed to stay above the key 3,900 level, wiping out the almost 1.5% gain on Monday.

Traders hoping for a quick end to aggressive rate hikes as global inflation cools got a rude awakening on Monday when Fed's Daly said she expects the central bank will raise rates to somewhere above 5%. Meanwhile, Fed's Bostic stated that policymakers should raise interest rates above 5% by early in the second quarter and then remain on hold for a long time.

- Those betting on slower hikes will have to wait until Thursday's US inflation report, which will be released almost a week after the latest jobs data showed that wage growth has slowed. The figures will be among the last such readings seen by policymakers before their meeting on January 31-February 1.