ALBANY, N.Y., JAN. 6 -- After months of political speechmaking and forays to Washington and Moscow, Gov. Mario M. Cuomo took to the ornate Assembly chamber here today and made clear that he will spend the next few months worrying about home-state issues.

In his annual State of the State address, the second-term Democrat unveiled several programs aimed at children. He proposed to combat rising dropout rates by guaranteeing a free college education to all seventh graders from low-income families as an incentive for them to finish high school.

Despite continued speculation that he may mount a late-starting bid for the White House, Cuomo stuck to such parochial concerns as garbage disposal and said little about the problems facing Washington.

"The governor consciously avoided speaking to national issues because he didn't want to increase speculation about the presidency," said Meyer S. Frucher, a key Cuomo adviser. Cuomo will be "pretty much bound to Albany" for the next three months as he tries to push his $40 billion budget through a divided legislature before the April 1 deadline, Frucher said.

By then, in the view of the governor and his aides, the Democratic presidential race will be all but over and so will the talk of a Cuomo candidacy. Cuomo said recently that the "worst thing" the Democrats could do would be to nominate someone other than one of the seven announced candidates.

In his speech declaring a "decade of the child," Cuomo said: "A staggering number of our children are undereducated, underfed . . . . Unless we act, many more of today's youth, the work force of the 21st century, will not be able to do the work.

"If compassion were not enough to encourage our attention to the plight of our children, self-interest should be."

Cuomo's "liberty scholarships" would guarantee a free education at a city or state university -- or make a comparable payment toward private tuition -- for all seventh graders from low-income families (about $14,000 or less for a family of four). Although today's address provided no budget details, Cuomo said the plan, when combined with existing scholarships, "would not be all that costly."

But Senate Republican leader Warren M. Anderson, who dismissed Cuomo's speech as "recycled stuff," was skeptical of the plan, saying: "It's going to cost an awful lot of money."

State lawmakers -- several of whom, including the Senate Democratic leader, were recently indicted in a payroll scandal -- have not forgotten how Cuomo embarrassed them last year by vetoing a weak ethics bill and forcing them to pass a stronger one.

Cuomo proposed to expand pre-kindergarten programs to all state schools within five years; to extend Medicaid coverage to 120,000 children from poor families, and to boost services for abused, neglected or mentally ill children. He also pressed an overhaul package for New York City's declining schools.

Cuomo said that half of a projected $800 million budget surplus should be spent on housing and the rest on rebuilding roads and bridges.

On other issues, Cuomo called for public financing of state political campaigns; an increase in the state minimum wage and jobless benefits; tougher penalties for crimes of racial and sexual violence; residential facilities for people with AIDS, and state divestiture from companies doing business with South Africa.

GOP leader Anderson preempted Cuomo Tuesday night by renewing the partisan warfare that marked the governor's relations with the legislature last year. "After five years of words rather than actions, the rhetoric is catching up to the governor," Anderson said.

Cuomo spokesman Tom Conroy called the attack "predictable, petty and partisan." But it mirrored some recent criticism here that Cuomo has not made progress on such thorny problems as housing and education.

While Cuomo's record includes multibillion-dollar investments in environmental cleanups and road repair, his accomplishments "look minute to most people," Democratic political consultant Bill Cunningham said. "They say, 'That's all small stuff, where's your legacy?' There's been no dramatic breakthrough because the problems he has are societal in nature."

Frucher disputed this assessment and called Cuomo "a builder" who has "laid tracks that lead into the 21st century. It is flashier to build the New York State Thruway than to rebuild the thruway, but rebuilding is just as important."

Unlike predecessors such as Nelson A. Rockefeller, who transformed the state with massive projects such as the Albany Mall, where the legislature convened today, Cuomo is not identified with one major issue.