The country is likely to hold early elections next month
In protest against Syriza's acceptance of the new austerity-heavy bailout 25 MPs have announced that they will break away to join a new Popular Unity party.
It will be lead by former energy minister, Panagiotis Lafazanis and it will be the third-largest group in the Greek parliament.
Yesterday, Tsipras confirmed he is resigning as Greek Prime Minister - paving the way for a general election to take place within the next 30 days.
There had been considerable speculation that an early vote would take place after Mr Tsipras secured a three-year, €86bn bailout package from creditors.
Although he was only elected prime minister seven months ago, several Syriza MPs expressed opposition to the rescue plan - not least because of the punishing austerity measures they will bring.
When Greece's parliament voted on the package last week, Mr Tsipras had to rely on opposition lawmakers for the bill to pass.
In a televised address to the nation, he said: "I feel the deep moral and political obligation to set before your judgment everything I have done, both right and wrong, the achievements and the omissions".
"The popular mandate I received on January 25 has exhausted its limits".
Mr Tsipras hopes a second Syriza victory in the upcoming election - which will likely be held on September 20th - will seal public support for the bailout package, and quell the backlash from party rebels.
However, before a polling date can be set, other parties will be given three days to try and form a new administration without Syriza.
The leader of Greece's second-largest party, New Democracy, has said it is his responsibility to exhaust all possibilities - and confirmed he is planning to meet with other political party leaders.
Syriza swept to power on a mandate of scrapping spending cuts and tax increases - but under Mr Tsipras, the party made a major U-turn by accepting strict austerity conditions in exchange for another bailout.
Despite this, he remains very popular with Greek voters, and in opinion polls before the bailout deal was finalised, he was far ahead of opposition rivals in opinion polls.
It is possible that Mr Tsipras could get a more favourable result in a general election that is held before voters feel the impact of the spending cuts and tax hikes which Greece must implement as part of the bailout deal.
The election will bring unwelcome levels of political uncertainty, and there has already been a detrimental impact on the Greek Stock Exchange.
Also on Thursday, Greece received the first instalment of loans from creditors, worth €13bn, enabling it to make a €3.2bn debt repayment to the European Central Bank.
Nick Malkoutzis is editor of economic and political analysis website Macropolis.
He told Newstalk Breakfast the resignation came as no big shock.