Three days after winning a third term with a less-than-anticipated percentage of the vote, New York Gov. Mario M. Cuomo (D) had some unsolicited advice for a man whose job many Democrats think he wants.

"I don't see him {President Bush} sending the same kind of energy into the economic struggle as he's sending over to the sands of Arabia," Cuomo said in an interview yesterday with Associated Press. "The economic threat to this nation is at least as great as the threat from {Iraqi President} Saddam Hussein, and everybody who is responsible knows it."

Cuomo added: "It appears from here that he prefers to deal with international geopolitics rather than the streets of our cities {or} . . . the domestic economic problems that have driven people into anger over taxes and spending."

While Cuomo reiterated that he has "no plans to run for president and no plans to make plans," other Democrats read his combative posture toward Bush as a preview of bigger things to come.

Told of the governor's remarks, Gary Fryer, his outgoing press secretary, quipped: "Welcome to round one."

"I think he has the instinct and the intellect to articulate a set of programs that benefits the middle class, and that's exactly what the Democratic presidential nominee in 1992 is going to have to do," New York pollster Douglas Schoen said.

Others argued that the prospect of a Cuomo presidential bid has been dimmed, not just by the 53 percent of the vote he received Tuesday (compared with 65 percent in 1986) against three weak opponents, but also by the huge budget deficit problems he now faces in New York.

Cuomo yesterday canceled a trip to Poland later this month so he could call the legislature into special session to plug an $824 million hole in New York's $30 billion general fund budget. As soon as that exercise is completed, he and the legislature will have to deal with a 1991 deficit projected at $2 billion to $3 billion -- and mounting.

Cuomo's budget woes in Albany have always been exacerbated by fractious relations with the Republican-controlled Senate. This year he had hoped his coattails might be long enough to elect a Democratic Senate; instead, the GOP padded its majority by one, to 35 to 26. Voters also narrowly defeated a $2 billion environmental bond issue Cuomo had made a crusade.

"He really got hurt in three ways on Tuesday," said Eddie Mahe, a campaign consultant to GOP nominee Pierre Rinfret, who finished a distant second Tuesday with 23 percent of the vote. "But his biggest problem is what lies ahead. I don't see how he can travel all over the country in the next year with the level of agony he's going to have to deal with at home."

Cuomo campaign spokesman Bill Cunningham blamed the governor's reduced victory margin on a 20 percent drop from the 1986 turnout in Cuomo's New York City base, and on economic hard times. "Our last three commercials had Cuomo warning the voters of the tough times ahead, and we may have paid a price for that," he said.

Privately, aides said that they do not expect Cuomo to consider whether to seek the presidency until next spring or summer, by which time they hope there will be a respite from the Albany budget wars.

Cuomo was not the only Democrat who made some moves yesterday that could be seen in a presidential light. Virginia Gov. L. Douglas Wilder's closest political adviser, state party chairman Paul Goldman, announced formation of a political action committee, the Committee for Fiscal Responsibility in 1992, that could become a vehicle for a presidential exploratory campaign.