Spokesman of a faction in the ruling Saenuri Party, which is not loyal to President Park, said the party leadership should immediately step down and the pro-Park faction should be dismantled, Xinhua news agency reported.
The party leadership is composed of loyalists to Park, whom the spokesman portrayed as "the men of Choi Soon-sil", a longtime confidante of Park, who was charged with using her sway.
Choi is accused of extorting donations from conglomerates and accessing secret government documents.
The impeachment motion was passed by 234 to 56 in the 300-seat National Assembly on Friday, indicating 62 votes in favour of Park's ouster came from the ruling party. There are 172 opposition and independent lawmakers.
The rift in Saenuri party, which has 128 parliamentary seats, became clear as internal fight between the anti and pro-Park clans called on each other to leave the party after the vote.
The party leadership called on former party chairman Kim Moo-sung and former whip Yoo Seung-min, who led the anti-Park faction, to defect from the party, issuing searing criticism.
Scores of pro-Park faction members held a meeting on Sunday night, agreeing to launch their formal council comprising of 50 legislators on Tuesday.
The ruling party's split imminent, that would make it harder for Park's party to regain power in the next presidential election, which is expected to be brought forward.
The election was originally scheduled for December 2017 as Park's single five-year term ends in February 2018.
Park was suspended from office, and her tenure would end if the two-thirds of the constitutional court's nine judges justify it within 180 days.
The court's decision would stabilise state affairs and minimise the power vacuum.