WARSAW, DEC. 20 -- Lech Walesa, who is to be sworn in Saturday as Poland's first popularly elected president, acknowledged today that he is having trouble finding anyone who wants to be prime minister.

Walesa asked the departing Tadeusz Mazowiecki to stay on until parliamentary elections in the spring. Two other candidates publicly backed out this week, citing differences with Walesa over the shape of a new government.

Ex-Solidarity union leader Walesa trounced Mazowiecki -- who led a Solidarity government that won international accolades for its economic efforts -- in the presidential election this month.

Immediately after his defeat, Mazowiecki resigned and accused Walesa of making populist promises in the campaign that would be impossible to keep. Mazowiecki remains in office in a caretaker role.

During the campaign, Walesa had accused his old Solidarity colleague of being "feeble" and incapable of dynamic leadership.

A spokeswoman for Mazowiecki said tonight that her boss had "no comment" on the request, which the prime minister first heard about today from the Polish press agency. She added, however, that she wanted "to stress that Parliament has already accepted our resignation."

Walesa, from the Baltic port of Gdansk where he has been struggling to put together a government, issued a statement today that left plenty of room for interpretation. He suggested "two logical concepts of a new government."

The first assumed that "nobody with a sense of responsibility" wants to be prime minister for just three months. So to find a good leader, Walesa said, "it would be necessary to postpone" parliamentary elections by at least one year.

This is not an option that any of the political parties is likely to favor, excepting the now powerless former Communists, who were guaranteed seats in the current Parliament under semi-free elections held in 1989.

The second option was to leave the old government intact, "with essential corrections," until spring elections.

Mazowiecki's confidants have scoffed at the idea of three-month caretaker role, arguing that Walesa should immediately be forced to take responsibility for expectations he raised during the campaign.

Walesa suggested on the stump that closures of money-losing state-owned factories could be postponed until the private sector was healthy enough to employ everybody.

Since the election, however, Walesa's advisers have said this is not what Walesa really means. They say that free-market reform, which would include factory closures and layoffs of hundreds of thousands of workers, is Poland's only option.

Part of the confusion surrounding the formation of a new government centers on the role to be played by Leszek Balcerowicz, the outgoing finance minister and father of the "shock therapy" program that has been lauded in the West as the most rigorous in Eastern Europe.

Walesa has made clear that he wants to keep Balcerowicz. Retaining him would be a signal to the international financial community that Poland intends to stick with policies that have won it generous debt concessions and about $10 billion in grants and loan credits.

According to participants in the haggling this week over who will be prime minister, Balcerowicz has insisted that he be given complete control of financial affairs. He also wants a strong enough voice in political affairs to prevent the weakening of his program.

In a recent interview, Balcerowicz said he would stay on in a government under Walesa only if there was no political interference in his program. His advisers released similar statements to the Polish press on Wednesday.

Today, Walesa urged all Poles to consider the prime ministerial options over the Christmas and New Year's holidays, after which he will make a final decision.