The Law and Justice (PiS) party leader had gone to Piłsudski Square on Friday, as he does every month, to mark the anniversary of the 2010 Smolensk air disaster, which killed 96 people including his twin brother, President Lech Kaczyński.
Police blocked him from reaching the monument, saying another group had already registered a gathering there.
Kaczyński and fellow PiS politicians laid their wreaths some distance away instead and at a separate memorial to the victims of the crash.
In response, the opposition leader accused the authorities of deploying what he called "the ruling party's paramilitaries, not the police" and said consequences would have to follow.
He suggested some form of "civic guard" might eventually be needed, and questioned whether the protesters present were acting on their own initiative or on behalf of a foreign power bordering Poland.
Asked about the remarks at a press conference, Tusk called Kaczyński "a warchoł" – a term with roots in Poland's old nobility, originally used for a hot-headed troublemaker who disrupted proceedings for his own ends.
He said it was "unwise" and "unacceptable" to repeatedly attack Poland's uniformed services, when everyone should instead be rallying behind the state and its institutions.
Tusk added that Kaczyński was exploiting the Smolensk tragedy yet again.
Poland's Interior Minister Marcin Kierwiński went further, calling the PiS leader's comments "scandalous" and a "disgrace" for a former deputy prime minister responsible for security to attack police officers in this way.
Separately, Warsaw police issued a statement insisting their officers had acted strictly within the law and remained a politically neutral force, saying their actions were guided solely by legal procedure and an assessment of the situation on the ground, regardless of participants' views or affiliations.
They added that the operation had been recorded on body cameras and CCTV.
Kaczyński said he hoped PiS would return to power after next year's parliamentary election, promising a "very deep reform" of the judiciary and state services if it did.
(ał)
Source: PAP