Senate budget-cutters have pronounced a death sentence for U.S. funding of the U.N. peace-keeping force in southern Lebanon, but the White House said this week it will work to continue the longstanding U.S. support.

Action to cut $18 million for the United Nations Interim Force in Lebanon (UNIFIL) originated with Sens. Warren B. Rudman (R-N.H.) and Ernest F. Hollings (D-S.C.), two sponsors of the Gramm-Rudman-Hollings deficit-reduction act, and went to the White House Thursday as part of the State Department appropriations bill. President Reagan signed the bill yesterday.

"We talked to staff who had been to Lebanon , to senators who had been there and to people at the State Department who spoke off the record," Rudman said. "Everybody we talked to said UNIFIL wasn't working and wasn't needed."

Rudman said UNIFIL is "typical" of government programs that cannot be terminated once in operation, regardless of effectiveness.

A spokesman for Hollings said, "UNIFIL is supposed to keep peace in Lebanon and obviously is not being very successful. We do not have enough money to finance symbolic actions."

The appropriations measure signed by Reagan provides funds to continue U.S. support of the international force until April, but the $18 million cut would end U.S. support then.

"Despite the difficulties the force has encountered in carrying out its mandate, we continue to view UNIFIL as a stabilizing element in south Lebanon, and it's playing a positive role there," White House spokesman Larry Speakes said.

Speakes said the administration has been in touch about the cutback with the government of Lebanon, which has strongly backed the U.N. force during its seven-year existence, with U.N. Secretary General Javier Perez de Cuellar and with the 10 nations that contribute the 5,800 troops on patrol duty.

The nations are Norway, Sweden, Finland, France, Italy, Ireland, Nepal, Fiji, Ghana and the Netherlands.

"We've assured them of our continued support for UNIFIL and our intention to seek restoration of funds cut by Congress," Speakes said.

UNIFIL was created largely at U.S. initiative in 1978 after an Israeli strike into southern Lebanon left the area unstable. The force of U.N. soldiers came into increasing conflict with Israeli forces and the Israel-backed South Lebanon Army after Israel's 1982 invasion of Lebanon.

Israeli Defense Minister Yitzhak Rabin, often critical of the U.N. force, said Wednesday that Israel thinks that the force is no longer needed.

"We informed all the states with whom we have ties that they can remove their troops" from the peace-keeping unit, he said.

In February, Rabin charged that UNIFIL troops had hampered Israeli raids on Shiite Moslem guerrilla strongholds and reportedly singled out the French for major criticism in remarks to an Israeli parliamentary committee.

U.N. officials said Israeli troops had "forcibly removed" French U.N. soldiers trying to prevent Israelis from demolishing homes of suspected guerrillas.

The United States, Lebanon and the nations contributing troops have asked that UNIFIL's area of responsibility be extended to the Israeli-Lebanese border.