Offering scant hope of fiscal relief in a time of recession and budget deficits, President Reagan has told state and local officials "there must be some pain for them also" until the economy revives and inflation abates.

In an interview focused on his views on federal-state-local relations, Reagan hinted strongly there would be further reductions in federal aid in next year's budget and little likelihood of achieving what he called "my dream" of returning some federal revenue sources to the states and localities. He promised such a return in his 1980 campaign, to compensate state and local governments for federal budget cuts.

Reacting to a plea from the Republican chairman of the National Governors Association, Richard A. Snelling of Vermont, that states be guaranteed no further cuts in federal aid below $46 billion for fiscal 1983 and 1984, in order to stabilize their own budget planning, Reagan said:

"I think it would be great if we could afford it . . . but I just think our emergency is so great, I don't know how we could hold back and wait for all of this." At another point, he said, "we have to straighten out this financial situation on the federal level" before guaranteeing as much or more aid to state and local governments.

The president said no final decisions had been made on the budget he will submit in January. But his comments reinforced warnings from Treasury officials that there would be no room in fiscal 1983 for the return of revenue sources from Washington, and a likelihood of further aid reductions.

A White House-Treasury task force has been studying the possibility of earmarking various federal excise taxes or relinquishing those tax sources for the states and local communities, as Reagan said he has long "dreamed" of doing. But budget realities have forced them instead to trim federal aid to state and local governments.

Reagan said he believed general revenue-sharing for the cities will have to be cut, along with other programs, but said he would not phase it out entirely. He vowed to press Congress to convert additional categorical programs into block grants as a way of saving money and giving more leeway to local governments on spending decisions.

But overall, the president did little to dispel what Snelling earlier this month called "the clouds of uncertainty" hanging over state and local governments as a result of the Reagan cutbacks.

The president, accompanied by his assistant for intergovernmental relations, Richard S. Williamson, answered questions for half an hour Thursday evening in an Oval Office interview with five reporters who cover the federalism beat.

The interview and an accompanying report on the first 10 months of Reagan's federalism initiatives were released for Sunday morning, as Republican governors gathered in New Orleans to discuss federal-state relations and their party's political situation.

Reagan drew strong support from the governors for passage of his economic program, but there have been growing differences between them over the federalism issues.

For example, Reagan told the interviewers he had little sympathy for the kind of "sorting-out" of federal and state responsibilities suggested by one of the most influential Republican governors, Tennessee's Lamar Alexander. Alexander and other governors would like to see Washington take full responsibility for welfare programs, while moving all education and most transportation financing to the states.

Reagan said education was "certainly" a local responsibility but said welfare could not be shifted to the national level without incurring "much more chance of waste and fraud." He said he would not rule out an increase in the federal gas tax for aid to state highway funds, but did not commit himself to include that in his budget.

While pointing to his record of meeting with more than 1,200 state and local officials in the past 10 months and offering further consultations, Reagan drew a sharp line against any proposals that would increase the federal role in adjusting interstate differences in economic growth or resources.

Asked if he thought it was "at all the responsibility of the national government to redistribute resources between states that are relatively well off and states that are not," he said, "no, I think that is up to the states."

He said one of the unique features of Americans' freedom is "the right of the citizen to vote with his feet." Where services are lacking, taxes are too high or the government is inefficient, he said, "the people will . . . either use their power at the polls to redress that, or they'll go someplace else," as industries do when confronted by "adverse tax policies."

Asked if that option was available to people "who have no money to move" and feel "trapped" in declining communities, Reagan said he would oppose any government "program for moving people" because of its element of potential compulsion. He acknowledged that some people feel so attached to an area they prefer to "sweat it out until jobs open up."

But he said, "Americans move more than anyone else," citing migration to such Sun Belt cities as Houston as the alternative that most young people would prefer to take.

In the same vein, he rejected criticism from Sen. David Durenberger (R-Minn.), the chairman of the Senate intergovernmental relations subcommittee, that the imposition of severance taxes by states with abundant energy and mineral resources is a way of passing their tax burden to people in consuming states.

The president said he thought such seeming inequities "balance out with everything else," because some states have farm surpluses and others produce automobiles and industrial products and the taxes on those products are paid by people in the energy-rich states.