The result of Sunday's presidential runoff leaves Tusk politically weakened and there are questions about whether his multi-party coalition can survive to the end of its term in late 2027.
Poland's Prime Minister Donald Tusk has said he would ask parliament to hold a vote of confidence in his coalition government after his ally, the liberal Warsaw mayor Rafał Trzaskowski, lost Sunday's presidential runoff.
Conservative Karol Nawrocki won the election, finishing with 50.89% of the vote.
"Regardless of how we evaluate the winning candidate, we should acknowledge his victory and congratulate his voters," Tusk said in a televised speech on Monday.
"I want to declare to you that I will not stop for a moment as prime minister of our government. The presidential elections have not changed anything here and will not change anything. We will cooperate with the new president where necessary and possible."
The result leaves Tusk politically weakened and there are questions about whether his multi-party coalition can survive to the end of its term in late 2027.
If he survives the confidence vote, it would show he still has a mandate to govern.
It is not clear when the confidence vote might take place.
Nawrocki will succeed conservative Andrzej Duda, whose second and final term ends on 6 August.
The close ballot had the country on edge since a first round two weeks earlier revealed deep divisions along the eastern flank of NATO and the European Union.
Although most day-to-day power in Poland lies with the prime minister, the president is able to influence foreign policy and, crucially, veto legislation.
Tusk, who came to power in late 2023 with a coalition government with a broad ideological divide, has been unable to muster enough support to fulfil certain electoral promises, such as easing abortion law.
He is expected to face further obstacles with Nawrocki as president.
The 42-year-old amateur boxer and political novice is supported by the conservative Law and Justice party (PiS) which governed Poland from 2015 to 2023.
Party leader Jarosław Kaczyński appealed on Monday to all political forces to support the formation of a technocratic government.
"Today we need a solution in the form of a technical government, which, like the president, will be non-partisan. The head of this government must be selected in talks with those who would be ready to support such a project. It would not have to be someone who has ties to us," he said.
"Individual ministries would be managed by specialists in specific areas of social life."