The proposals are aimed at staving off financial collapse and preventing a possible exit from the eurozone.
Eurozone finance ministers will examine the new proposals, which include pension cuts and tax rises, ahead of a full EU summit on Sunday.
Correspondents say Mr Tsipras’s new plan contains many elements rejected in a referendum last Sunday.
He is likely to face opposition from the left of his own Syriza party, according to The BBC.
However, a parliamentary spokesman for Syriza, Nikos Filis, said he was confident parliament would give the government the mandate to negotiate the new bailout package.
The coalition government has 162 seats in the 300-strong parliament and also has the backing of many opposition MPs.
Greece’s parliament is likely to give approval to negotiate the deal, because support from the opposition will outweigh critics on the far left of the governing Syriza party.
But with the tax hikes and pension reforms very similar to what the creditors were originally demanding, what has Alexis Tsipras achieved by holding last Sunday’s referendum?
Possibly some concessions on debt relief and growth measures – or possibly by showing Greeks that he was fighting until the 11th-hour, it will strengthen his hand here and allow him to implement the reforms.
There will, though, be plenty of critics who say he was elected because he promised to end austerity and he won a “No” vote just last Sunday. And now he’s gone back on virtually every pledge.
Mr Tsipras convened a meeting of Syriza ahead of the parliamentary debate.
A government official quoted him as telling the party’s lawmakers that the referendum had given him a mandate to seek a better deal but not to leave the eurozone.
“We are all in this together,” he was quoted as saying.
The prime minister submitted the proposals to Greece’s creditors – the European Commission, the European Central Bank and the International Monetary Fund – by the Thursday deadline they had set.
Energy Minister Panagiotis Lafazanis on Thursday urged the government not to agree to a bailout that would “surrender, loot and subjugate our people”.
He said the “No” vote in last Sunday’s referendum, when Greeks rejected creditors’ terms for a new bailout, should not be turned into a “humiliating ‘Yes'”.
Further rallies are planned in Athens on Friday, both backing and opposing the terms of a new bailout.
There has been no immediate response to the new proposals from the creditors.
However, Malta’s Prime Minister Joseph Muscat, who on Tuesday was highly critical of Greece’s failure to provide new plans, tweeted: “At first glance, Greece proposals provide a basis for discussion.”
The plans will be discussed at technical level on Friday, before a meeting of eurozone finance ministers in Brussels on Saturday. There will then be a meeting of Eurogroup leaders on Sunday afternoon and a full EU summit two hours later.
European Council President Donald Tusk has described the situation as “maybe the most critical moment” in EU history.
Greece’s creditors have already provided more than €200bn in two bailouts since a rescue plan began five years ago.
The second bailout expired on 30 June.
For the third bailout, Greece is reportedly seeking €53.5bn and a restructuring of its huge debt burden.
Greece’s banks are still closed and the €60 (£43; $66) daily limit on cash machine withdrawals, imposed on 28 June, remains in force.
