After the game, Mr Kramnik said he was "a bit disappointed" but hoped a rematch could be arranged in a year or two.

"With more time to prepare, I still have a chance," he said.

In 2002, Mr Kramnik held Deep Fritz to a draw after eight games, but the chess software has since been updated, calculating millions of positions every second.

In October, Mr Kramnik defeated Bulgaria's Veselin Topalov to become the undisputed world chess champion for the first time since 1993.