President Bush's new budget will ask Congress to give states new responsibility for administering an estimated $15 billion in federally funded programs -- in job training, rural health, education, highways and law enforcement, according to governors briefed yesterday on the contents of the plan.

The proposal, which could also give state governments responsibility for allocating administrative costs of some human services programs, was greeted warmly by governors meeting here. White House Chief of Staff John H. Sununu assured them during a luncheon meeting that the federal government would continue to fund the programs for at least five years.

Several governors who attended the session said they will now seek to convince members of Congress that they want the flexibility they see in the White House proposal.

Sununu said the budget plan will list $22 billion in federal programs for the states and propose that state officials and Congress include the bulk of them in a block grant program. He estimated the grants would amount to about $15 billion.

"They can add anything they want to the list or subtract anything they want from the list," he said. "The list is just illustrative."

White House officials have sought to reassure state officials that the new plan is not just a revised version of President Ronald Reagan's 1982 proposals that would have reduced funding for entitlement programs and passed the responsibilities on to the states. That plan, dubbed New Federalism, failed to win support either in Congress or at the state level.

Several governors interviewed yesterday said they understood the new proposal to be a more acceptable approach, one that would allow states to steer funds where they are needed most.

"There's enthusiasm for the idea," said Washington Gov. Booth Gardner (D), the chairman of the National Governors' Association. "But also caution based on previous experience."

"Everybody's skeptical about whether Congress will go along with" the president's plan, said South Carolina Gov. Carroll A. Campbell Jr. (R).

But Iowa Gov. Terry E. Branstad (R) suggested that members of Congress watching governors and state legislatures redraw congressional district lines this year may be more willing to listen to pleas from the states.

Along partisan lines, Democrats were more cautious than Republicans about the block grant plan. "Having been in politics as long as I have, I'm a little cynical about how to get Congress to go along with this approach," said Georgia Gov. Zell Miller (D).

New Jersey Gov. James J. Florio (D) warned that the new approach will not mean new money for the states, as many federally funded domestic programs will be grouped under a common budget ceiling as part of last year's deficit-reduction agreement.

"We're dealing with an artificial situation," he said. "Do you want more discretion? Of course you do. But discretion to deal with less money? That's not doing us a favor."

Delaware Gov. Michael N. Castle (R) noted that governors have been most unhappy with the expensive federal mandates attached to state-administered programs like Medicaid. The president's proposal, he said, responds to "exactly the kind of thing we have been complaining about."

"We are the managers," said Wisconsin Gov. Tommy G. Thompson (R), who argued in an interview that states can run federal programs better. "Congress doesn't have to manage anything except their own offices."

Arkansas Gov. Bill Clinton (D) said the proposal could signal a new level of cooperation between the states and the White House. "Why should we be viewed as some kind of interest group going hat in hand" to the federal government, he "Everybody's skeptical about whether Congress will go along."

-- Carroll A. Campbell Jr., South Carolina governor

asked. "They've been draining state budgets for four years now."

Gardner said governors will support the program as long as a formula is developed that funnels the money to individual states fairly and allows funding for certain programs to rise as needs increase.

A senior administration official said yesterday the White House would like to convince the governors and the National Conference of State Legislatures to urge House Speaker Thomas S. Foley (D-Wash.) and Senate Majority Leader George J. Mitchell (D-Maine) to ease the proposal's path through Congress, perhaps by establishing separate committees to consider it.