Lafazanis, who formally split from Syriza to found Popular Unity along with 24 other rebel lawmakers, said he would use the full three days allowed under the constitution.
However, he said he would merely promote, before the inevitable election, his opposition to the painful economic policies that the euro zone and IMF have imposed on Greece over the past five years in return for bailout loans.
"We do not have any illusions that any anti-bailout government can be formed from this parliament," he told reporters. "We will use this mandate to show that the only thing that is in the interest of the Greek people is a new anti-bailout parliament and government."
Read MoreEurope may find itself relying on success of Greece's Tsipras
The opposition appears in no hurry to face voters who are returning from summer holidays to find their living standards cut yet further by value-added tax increases and the imposition of a "solidarity" income tax - measures under the bailout deal that may erode Tsipras' popularity.
Tsipras, who wants elections next month, lost another former ally on Monday. Tasos Koronakis resigned as secretary of Syriza's powerful central committee. Koronakis, who is not a member of parliament, appeared to be protesting about Tsipras' leadership style and is unlikely to join the breakway party.
However, his resignation underlined Tsipras' problems in holding together Syriza, which had 149 of the 300 seats in parliament before the split.
Tsipras quit after only seven months when he lost his majority due to the rebellion led by Lafazanis. He had to rely on temporary support from pro-bailout opposition parties to get the 86 billion euro ($99 billion) program through parliament, and is pushing for early elections in the hope of returning to power with a majority.
Analysts believe Tsipras is likely to win but without a majority. However, he rejected a post-poll deal with Greece's traditional mainstream parties such as conservative New Democracy. According to a statement from his office, he told senior party officials he ruled out co-operation "with the systemic forces of the old political system".
When Lafazanis has exhausted his three days, President Prokopis Pavlopoulos can appoint a caretaker premier and call elections within 30 days.
Read MoreGreek ruling party heads towards split before bailout vote
New Democracy leader Vangelis Meimarakis acknowledged earlier on Monday that he could not form a government. He accused Tsipras of taking Greece down a "destructive path" by pushing for polls when its future in the euro zone remains far from secure.
"He has acknowledged in parliament that the Grexit ghost is still hovering over the country," Meimarakis told the president, suggesting Tsipras would still need coalition partners after an election. "He thinks he can be the first party in the next parliament - I'm wondering with whom he wants to do this, since he doesn't want to see any of us again."
The centrist To Potami party - a pro-euro party that has supported Tsipras in bailout votes in parliament - and the right-wing Independent Greeks party, currently Tsipras' ally, are both considered potential coalition candidates.