ALBANY, N.Y., JUNE 3 -- Gov. Mario M. Cuomo surprised no one today when he told cheering supporters that he will seek reelection.

Cuomo, a potential 1992 Democratic presidential contender, was expected to win virtually unanimous support from delegates at the state Democratic convention on Monday. The popular state chief would then run against Pierre Rinfret, a millionaire economist and political newcomer chosen by Republicans last week.

If he wins, Cuomo would serve his third four-year term as governor.

"The truth is, Matilda and I don't want to do anything else," Cuomo said as he and his wife visited the Empire State Plaza convention center where the Democratic gathering will be held.

Deborah Ishlon, a Rinfret spokeswoman, said the Republican candidate would make no immediate comment on Cuomo's reelection announcement.

Cuomo refused to promise that he will serve the full four-year term if reelected, keeping open the possibility of a 1992 presidential effort.

"That wouldn't work at all," said Cuomo of such a pledge. "What would make you believe it?"

Facing his third straight year of deficits, Cuomo recently approved a record $1.8 billion tax increase package to keep his budget balanced.

The Canadian-born Rinfret, a resident of Manhattan, has promised to make Cuomo's handling of New York's economic problems a cornerstone of his campaign. He has already begun comparing Cuomo to lame-duck Massachusetts Gov. Michael S. Dukakis (D), who has grappled with state budget problems almost continuously since he lost the 1988 presidential race.

Cuomo, 57, is the son of Italian immigrants and grew up behind his parents' small grocery in Queens.