With both sides eager to conclude budget talks this week, the White House and congressional Republicans met yesterday in an unusual weekend session to try to narrow their differences over interior spending and a handful of other key issues that are blocking a final deal.

While conflicts about overall spending are fast evaporating, Republicans and the administration remained far apart over hiring additional teachers and police officers, paying nearly $1 billion of back United Nations dues and the details of President Clinton's "Lands Legacy" initiative to acquire environmentally and culturally significant land that is threatened by development.

White House Budget Director Jacob "Jack" Lew left the meeting last night saying he was disappointed that more had not been accomplished. "We're a long ways from everything being decided right now," he said.

The dispute over Clinton's demand for another installment in hiring 100,000 new teachers and his land acquisition program were the most contentious issues.

White House Chief of Staff John D. Podesta angered Republicans yesterday by declaring during a televised appearance that Clinton would not budge in his demand that Congress spend $1.4 billion to hire 30,000 more teachers. And Clinton refuses to agree to the GOP's approach of giving local school boards the option of using the money for other purposes. The White House contends that hiring more teachers to reduce the average class size is the most important thing that can be done to improve the quality of education.

"Realistically, I think we are not prepared to go home until we do get more teachers and lower class size," Podesta said on NBC's "Meet the Press."

Sen. Arlen Specter (R-Pa.), chairman of the Senate appropriations subcommittee with jurisdiction over education spending, warned that White House intransigence might force the Republicans to dig in their heels. "That makes me pretty determined to keep what the Congress has done," Specter said before entering the negotiating room in the Capitol.

The administration is equally adamant about funding for the Lands Legacy program, which would buy New Mexico ranch land, California desert and parts of the Florida Everglades. The White House has sought about $700 million for land acquisition and related activities, but Congress approved only $266 million. Yesterday, the Republicans offered to boost overall interior spending by $338 million--or a total of about $14.8 billion--for land acquisition and other Interior Department programs. But they rejected a last-minute administration proposal to make the Lands Legacy program a trust with dedicated funding.

"We're closer on numbers, but we are not going to authorize a new entitlement," declared Sen. Slade Gorton (R-Wash.), a senior appropriator with jurisdiction over interior spending.

Republicans and the administration reported some progress in resolving their differences over the interior bill, which Clinton vetoed last month. However, they have yet to settle differences over a number of environmental "riders" dealing with the dumping of mining waste, royalties paid by companies that extract oil and natural gas from public land and grazing on federal lands.

GOP leaders appear prepared to water down some of those provisions that affect mining, grazing and other industries in the West, which the administration contends would harm the environment. GOP leaders also are likely to break the impasse over the unpaid U.N. dues by requiring that antiabortion forces relent on their efforts to link the dues to restrictions on international family planning programs.

A deal worked out late last week that provided Clinton with $2.6 billion more for foreign aid and to underwrite the Wye River Middle East peace accords raised hopes that Republican leaders and the White House could resolve many of the remaining issues over the weekend, with an eye to a final deal by midweek.

Clinton is scheduled to depart at the end of the week on a 10-day trip to Central Europe, and members of Congress are anxious to adjourn by Wednesday or Thursday--producing what an administration official last night described as a "natural deadline."

"We could have it worked out by then," said Senate Appropriations Committee Chairman Ted Stevens (R-Alaska), who hosted yesterday's sessions in his committee office.

"These guys have the smell of jet fuel in their nostrils," said a House GOP appropriations aide in describing congressional eagerness to leave for the Veterans Day holiday.

However, the talks are complicated, and yesterday's session to discuss three of the five unresolved spending bills for the fiscal year that began Oct. 1 produced only modest progress. Until now, the Republicans have been reluctant to engage in closed-door meetings with administration officials, fearing a repeat of last year's talks that ended with Clinton extracting billions of dollars in concessions.

Lew, the White House budget chief, noted recently that the two sides made the most progress on the foreign aid bill when they didn't talk face to face but instead exchanged offers over the telephone or by fax.

"Some progress was made today, but we are a long ways from a done deal on any of the bills we're talking about," said Linda Ricci, a spokeswoman for the Office of Management and Budget. "We certainly hope this can be resolved quickly, but on the other hand, we're also prepared to do week-to-week continuing resolutions if that is necessary to resolve these important differences and to get a commitment to reducing class sizes."