Asian shares climbed on Tuesday, benefiting from a decline in bond yields and bolstered by the Federal Reserve's dovish statements, along with a drop in oil prices following Monday's surge.

European and U.S. markets also appeared poised for higher openings, with FTSE futures up by 0.78%, and E-mini futures for the S&P 500 index showing a 0.07% gain at 0504 GMT.

According to Reuters, MSCI's index for Asia Pacific stocks, excluding Japan, initially increased during the morning and later settled with a 0.81% gain.

On Monday, key Federal Reserve officials indicated that the increasing Treasury yields might deter the central bank from implementing further rate hikes, which contributed to a rebound in bond prices. This rebound came after both U.S. and Tokyo bond markets had been closed the previous day.