The shake-up came three days after Mr. Varoufakis drew fierce criticism from his eurozone peers at a meeting in Riga, Latvia. The other finance ministers voiced frustration over a lack of progress in talks to continue extending loan money that Greece desperately needs to avoid a default that could otherwise happen in coming weeks. Part of their concern is that a default by Greece could force the country from the euro currency union, threatening the ability of the bloc to hold itself together.

Most European officials have said that they want to avoid such a prospect, despite having built firewalls against financial contagion since the last major Greek crisis in 2012. But some indicated after the Riga meeting that a “Plan B” for Greece should be considered in case talks collapse.

Although Mr. Tsipras’s office on Monday expressed support for Mr. Varoufakis, saying he had been “systematically targeted in the international press,” some Greek news media interpreted the move as a way of sidelining the finance minister.

Opponents of the government led by Mr. Tsipras’s party, Syriza, have publicly criticized Mr. Varoufakis for weeks. On Monday, a prominent conservative and former foreign minister, Dora Bakoyannis, called for Mr. Varoufakis to resign, saying he was a “drag” on the debt negotiations and was undermining Greek national interests.

Mr. Varoufakis was named finance minister in January largely on his international reputation as an economist who had long led a public campaign against the belt-tightening terms of the international bailout program agreed to by a previous government. After giving Mr. Varoufakis such a prominent stage, Mr. Tsipras might find it politically awkward to force him out. That could be a reason for saying Mr. Varoufakis will lead the negotiations, even as less polarizing figures are put in charge of the day-to-day discussions.