"We have just held a faction session, when all those present signed their resignations," said Andriy Shevchenko from Tymoshenko's faction. "This is a political signal so far that there are 150 members of the Supreme Rada who are ready to give up their mandates if need be and thereby give the president additional grounds to dissolve parliament."
The lawmaker added the procedure to finalize the resignations had not been launched so far.
The Constitution says 150 lawmakers have to resign for proceedings to disband the legislature to be launched. The faction led by former Premier Tymoshenko comprises 125 members, and Our Ukraine has 77 seats in the 450-seat Supreme Rada. Eleven members from both factions defected to the majority coalition in late March, triggering a new wave of tensions in the ex-Soviet state.
In comments on the report, Valentin Matveyev, first deputy chairman of the Communist faction - within the majority coalition along with the Socialists and the Party of Regions - said "our colleagues are bluffing" as they did not recognize the legislature and had therefore nowhere to file their resignations.
But Our Ukraine said in a statement: "Since laying down deputy powers is impossible now, when the Supreme Rada has been dissolved, writing notices to quit the faction is the only way [of resigning from parliament]."
The majority coalition has continued working, referring President Viktor Yushchenko's April 2 order to disband the legislature and call early elections to the Constitutional Court.
The court began the examination Tuesday and continued work Wednesday despite a blockade of the court building by thousands of opposition and coalition supporters. Judges said it would take about 10 days to decide on the matter.
Yushchenko and his archrival Yanukovych have said they will obey any court decision.
But Tymoshenko said Wednesday her bloc would not recognize a ruling by the court, saying its judges represented political parties and most of them were corrupt. She called the court session a farce and "a seizure of power by Yanukovych's clan."
Echoing the statement, Our Ukraine leader Vyacheslav Kyrylenko said the two factions would block parliamentary activities irrespective of a court decision by ignoring plenary sessions.
"Parliament is only legitimate if two-thirds of the deputies or more are present," Kyrylenko said.
A flamboyant leader of the 2004 "orange revolution" that swept Yushchenko to power, Tymoshenko also called for fresh protests.
"I want to call on people across Ukraine, no matter where you live, to come to Maidan [square]. We will continue our Maidan [protests] until early elections," she said.
Yanukovych's backers have so far dominated central Kiev since the presidential order, and their rallies have been peaceful.
Opposition members claimed earlier Wednesday that police had beaten up their fellow supporters near the Constitutional Court building, and that the ruling coalition stood behind the police actions. Yanukovych's Party of Regions dismissed the accusations as provocations.