The Costa Rican chapter of the continuing saga or Robert Vesco has come to an end - almost.

President Daniel Oduber's announcement yesterday that the fugitive U.S. financier has been asked to leave the country climaxes five stormy years during which this small Central American republic has been the focus of steadily growing international attention.

Vesco faces civil and criminal charges in the United States, stemming from allegations that he looted $224 million from the Investors Overseas Services mutual funds in the early 1970s and that he made a secret $200,000 contribution to the 1972 reelection campaign of former President Nixon.

Oduber's statement on Vesco came only a few hours after a State Department spokesman in Washington said Vesco should be extradited to the United States.

U.S. officials touring Latin America with Rosalynn Carter said that Terrence Todman, assistant secretary of state for inter-American affairs, had discussed the Vesco case with Oduber when Mrs. Carter was in Costa Rica last week. Todman reportedly said the United States wanted Vesco extradited.

Oduber's request that Vesco leave is widely interpreted here as a last-ditch effort to salvage the 1978 presidential election for his National Liberation Party.The recent political scandal that disclosed Vesco money indirectly behind Oduber's successful 1974 campaign appears to have greatly weakened the party's credibility with the more than one million voters.

Reached by phone from Washington, Vesco said he has no plans to leave Costa Rica. He said Oduber's statement was misinterpreted. Vesco said he and Oduber made "an agreement" before Oduber's speech, that "I would clear up the local litigation, then I might contend with the foreign suits."

[Vesco dismissed press speculation that he would try to become a Costa Rican citizen to avoid extradition by U.S. authorities. "I have stated publicly that I will not apply for Costa Rican citizenship until the legal situation here is clarified," he said.]

Meanwhile, in continuing financial revelations about Vesco, companies connected with him have been accused in the Costa Rican press of making a profit of more than $10 million from the nationalization in 1975 of local gasoline distributors.

The apparent announcement of Vesco's departure came less than three weeks before the financier becomes eligible for Costa Rican citizenship - almost five years after he arrived here from the Bahamas, where the successfully fought a U.S. extradition attempt. A second try to extradite him, this time from Costa Rica, failed in 1973.

An aide to President Oduber said yesterday that the Costa Rican government allowed Vesco to remain here five years because the U.S. extradition attempt in 1973 was not taken seriously.

"It was done so badly that it gave us the impression that the United States didn't want him back," presidential aide Rodrigo Furnier said.

Furnier also said that before he can leave, Vesco must meet two conditions imposed by Oduber. He must provide a full accounting of his Costa Rican investments and he must settle a suit brought by a local architect who claims he lost $200,000 investing in IOS.

It is not clear where Vesco would go. He must choose carefully to avoid going where he would be vulnerable to extradition. Many countries would not welcome him even though he would bring along the millions he allegedly looted form IOS.

There are rumors that Vesco has sent out feelers to the governments of Andorra, Paraguay, and the Cayman Islands.

[Vesco scoffed at these rumors in the telephone interview.]

Before going to Costa Rica, Vesco lived in Nassau, Bahamas, and he still has financial interests - in the Bahamas.

Bahamian Prime Minister Lynden O. Pindling, who with his friends enjoyed Vesco's financial resources while he was in Nassau, faces a tough election July 19 and a major issue of the campaign is alleged corruption in the Pindling government.

Verco's pervasive influence here has acutely embarrassed Costa Rica, one of the few remaining democracies in Latin America.

In what appears to be a mini-version of Vesco's alleged takeover of IOS in 1971, Vesco companies reportedly maneuvered themselves into position to reap millions of dollars from Costa Rica's 1975 takeover of gas companies.

According to reports in the local press this week, the complex gas-deal machinations involved four local companies said to be controlled by Vesco.

In addition, local court testimony in a suit growing out of the controversial nationalization cites involvement of President Oduber, fomer President Jose ("Pepe") Figueres, Figueres' son Jose Marti, and two Vesco associates in the complex $10.75 million deal.

Though the nationalization was not announced by Oduber until 1975, Vesco related companies had apparently long before obtained control of the firms which were to be bought out.

The gas takeover revelations come on the heels of a series of startling statements by former President Figueres to The New Republic linking Vesco to Oduber's 1974 successful presidential drive.

October has denied receiving money from Vesco, but admits that his National Liberation Party accepted a Oduber has denied receiving monloan from a Figueres company. He claims the loan was repaid when the party realized the Figueres firm had been financed by IOS.

Washington Post staff writers John F. Berry and Susanna McBee contributed to this account.