After two days of persuasion by the United States and the Soviet Union, the two contending sides in Angola's 15-year-old civil war indicated yesterday that they expect to achieve a cease-fire early next year.

Jonas Savimbi, leader of the U.S.-backed rebels fighting Angola's Marxist government, made the announcement following a White House meeting with President Bush.

"I think we are real close. . . We hope to work hard in order to achieve a cease-fire early next year and to have elections by the end of 1991," said Savimbi, who heads the National Union for the Total Independence of Angola (UNITA).

On Wednesday, Savimbi conferred here with Soviet Foreign Minister Eduard Shevardnadze, and Secretary of State James A. Baker III met with Angolan Foreign Minister Pedro de Castro Van Dunem. Their discussions sought to further current peace talks in Lisbon under the sponsorship of Portugal, Angola's old colonial ruler.

Yesterday, UNITA Vice President Jeremias Chitunda and Lopo do Nascimento, a member of the Angolan Community Party central committee, conferred all day in a unique five-party meeting with Herman J. Cohen, assistant secretary of state for African affairs; Yury Yukalov, African affairs chief of the Soviet foreign ministry; and Antonio Monteiro, chief of cabinet to Portugal's state secretary.

In a joint statement afterward, Cohen, Yukalov and Monteiro said: "We believe that significant progress has been made, and that the prospects for a successful sixth round of negotiations in Lisbon early next year have been enhanced. We were favorably impressed by the friendliness of the atmosphere created by the two Angolan parties as well as by the seriousness of their approach to the negotiations."

The United States has been providing an estimated $40 million a year in covert lethal aid to UNITA, and U.S. officials contend that the Soviets gave the Angolan government at least $500 million in military assistance this year.

The cease-fire, Cohen said yesterday, is "envisaged as an agreement by both sides to refrain from receiving lethal material from any source."

He said the improved prospects for peace were due to a combination of internal and external factors. Internally, Cohen asserted, "there is exhaustion from 15 years of war. Both sides now are aware that they cannot achieve any more of their aims through the military option. They also are being pressured by their followers on both sides to settle the conflict peacefully."

He cited as the main external factors the new determination of the United States and the Soviet Union to cooperate in ending regional conflicts, the withdrawal from Angola of Cuban and South African forces and the world-wide disenchantment with Marxism as a workable system. The Angolan government is moving from rigid Marxist doctrines toward what it promises will be multiparty democracy.