SHANGHAI, Nov 21 (Reuters) - China's major state-owned banks were seen exchanging yuan for U.S. dollars in the onshore swap market and selling those dollars in spot currency markets this week, two sources told Reuters on Tuesday.

The yuan has gained 2% in the past week, to stand at levels around 7.13 to the dollar - its highest in nearly 4 months - and the big state banks have continued to sell dollars for yuan this week, the sources said.

State banks are often suspected of stepping into the currency market on behalf of the authorities, but the timing is unusual as they would usually sell dollars when the yuan is under pressure to depreciate.

Their action over the past week came amid broad dollar weakness, leading dealers to suspect the aim was to accelerate the yuan's recovery. (Reporting by Shanghai Newsroom Editing by Vidya Ranganathan & Simon Cameron-Moore)