The dispute centres on a political association founded by former Prime Minister Mateusz Morawiecki, one of the party's most prominent figures, state news agency PAP reported.
Kaczyński said the party's leadership would meet on Tuesday to formally acknowledge the resignations.
The announcement followed a Thursday midnight deadline for lawmakers to declare that they did not belong to any outside political associations or face expulsion from the PiS party.
Kaczyński said the dispute involved not only Morawiecki's Development Plus association but also what he described as proposals made several weeks ago to split the party.
"In these circumstances, we could only view the association as part of a plan to divide our party," Kaczyński said.
He added that lawmakers had been aware of the consequences of refusing to sign a declaration renouncing membership in outside associations.
According to Kaczyński, the party leadership made significant concessions, including dropping its demand that the Development Plus association be dissolved.
Instead, it proposed that the association suspend its activities until after next year's parliamentary election, but Kaczyński said the offer was rejected.
The departures are the latest sign of growing internal tensions within the conservative party, which governed Poland from 2015 until losing power in the 2023 parliamentary election.
Morawiecki said on Friday he had refused to sign what he called a party "loyalty declaration" and offered to step down as one of PiS's deputy leaders.
(gs)
Source: PAP