SHANGHAI/BEIJING, Feb 20 (Reuters) - China's major state-owned banks were seen selling dollars on Tuesday, three people with knowledge of the matter said, in an attempt to arrest weakness in the yuan in the wake of a deep cut to the benchmark mortgage rate.

Chinese state banks were actively swapping yuan for dollars in the onshore swap market before quickly selling those greenbacks in the spot market to support the local currency, the sources said.

The state bank action comes as the Chinese yuan weakened past the psychologically critical 7.2 per dollar level on Tuesday after China announced its biggest ever reduction in the benchmark mortgage rate to revive the crisis-hit property market.

The sources declined to be identified because they were not authorised to speak publicly about market trades.

Chinese state-owned banks usually trade on behalf of the nation's central bank in the foreign exchange market, but they also trade on their own behalf.

(Reporting by Shanghai and Beijing Newsroom. Editing by Vidya Ranganathan and Shri Navaratnam)