Mariusz Kaminski and Maciej Wasik were sentenced to two years' jail last month for abuse of power when they led an anti-corruption office in 2007.
Following the arrests, the new interior minister Marcin Kierwinski wrote on X: "Everyone is equal before the law."
The arrests highlight the political turmoil between the Law and Justice (PiS) party and the new pro-EU coalition.
The men, who were elected PiS MPs in October, refused to recognise last month's court decision because President Andrzej Duda, a PiS ally, pardoned them for the crime in 2015. Mr Duda has also said he does not recognise the court's ruling because he insists his pardon remains valid.
The pair have been stripped of their parliamentary mandates, but both they and President Duda insist they remain legally elected MPs because of the pardon.
On Monday evening, the court issued a warrant to police to detain the men. Despite this, Mr Duda invited both to Warsaw's Presidential Palace on Tuesday morning to attend a ceremony to swear in two of their former colleagues as presidential advisers.
Several hours later, they emerged from the palace to speak briefly to reporters, all the while remaining inside its grounds. Mr Kaminski said they will be "political prisoners" if they are arrested and thanked Mr Duda for his support.
"We are dealing with a very serious state crisis. A grim dictatorship is being created," Mr Kaminski said. They then returned inside the palace as the political theatre unfolded.
Moments later, Prime Minister Donald Tusk told a news conference the situation was "unbelievable". He said the court's ruling must be respected and suggested President Duda was helping the men evade justice.
"There is no rulebook for the prime minister or interior minister on how to act when convicts are in the Presidential Palace. This is clearly taking advantage of a situation in which no one will use force against such an institution as the president," he added.
Following the arrests, several hundred PiS supporters demonstrated outside the palace in support of the men.
Last year, the Polish Supreme Court ruled Mr Duda's 2015 pardon was invalid because it was issued while the men were appealing against their conviction, ie before the original conviction was final. Mr Duda disputes that and insists the pardon is still binding.
To complicate matters, the Constitutional Tribunal and a new Supreme Court chamber, both of which are staffed by judges nominated by PiS, have ruled in favour of Mr Duda.
Mr Tusk said Mr Duda could resolve the stand-off by pardoning the men again, now that the ruling is final. But that would call into question the legal status of the initial pardon.
Mr Tusk's coalition took office last month pledging to undo PiS's changes to the judiciary, public media, and civil service that the European Commission and many other international bodies say have undermined the rule of law in Poland.
One of its first acts was to reform the state TV, radio and news agency that PiS had transformed into a propaganda mouthpiece for its government.
But its methods were similar to PiS's, first using a government minister to sack media boards and install new people ahead of planned legislative reform.
The Helsinki Foundation for Human Rights acknowledged PiS had made it legally difficult to reform the public media, which it said required "urgent reform" because it had become "a propaganda mouthpiece" under PiS, but said the new government's changes "raise serious doubts".
Former PiS prime minister Mateusz Morawiecki told the BBC Mr Tusk's government talked loudly about democratic standards but fell well short in practice.
"We are witnessing an unprecedented attack on the rule of law. Tusk's government decided it could take over public television and media by force. This has nothing to do with democratic standards. We have not seen such brutal government action since communism. It is all the more outrageous that this is done by people who have such slogans of democracy on their lips," Mr Morawiecki said.
Given PiS's record of controlling state institutions while in office, many Tusk supporters argue such accusations are the height of hypocrisy.
By Adam Easton
BBC News, Warsaw