Parliament resumed on Monday to pay respects to victims of the December 14 massacre, when 15 people were killed by gunmen targeting a Jewish celebration.
The government initially planned to introduce an omnibus bill criminalising hate speech and strengthening gun laws, before widespread opposition forced it to split the legislation into two.
The prime minister said Labor had tried to implement measures cracking down on anti-Semitism which has been demanded by the coalition.
Labor wants to pass hate speech reforms through the upper house on Tuesday evening.
Asked if Tuesday was the final chance to pass hate speech laws, Mr Albanese replied "correct".
"We're not a government that puts things up over and over again to see them defeated," he told ABC radio Melbourne.
The Greens are opposed to the hate speech measures, concerned they will risk political freedoms such as the ability to protest Israel's war in Gaza, as well as changes increasing the power of the home affairs minister to cancel visas.
Cabinet minister Murray Watt said the government was negotiating with the coalition on the hate reforms, after Opposition Leader Sussan Ley last week labelled them "unsalvageable".
"We don't think it serves the country's interests to have an acrimonious debate about legislation if we know in advance that it's not going to pass," he told ABC's RN on Monday.
"That's why our focus, particularly over the next 24 hours, is going to be persuading the coalition to vote for the kind of things that they've been demanding that we act on.
"We are again very hopeful that they will support those laws."
The parliament is being recalled as the first two major polls of the year show Mr Albanese's personal standing with voters taking a hit since the Bondi tragedy.
The first Newspoll conducted for The Australian since November shows Mr Albanese's personal approval rating down five points to 42 per cent and Opposition Leader Sussan Ley's up two to 28 per cent.
The Resolve Political Monitor poll for Nine Newspapers, conducted in the aftermath of the Bondi massacre, shows Mr Albanese's approval rating down five points to 35 per cent.
It has Labor's primary vote down two points to 30 per cent, followed by the coalition (steady at 28 per cent), One Nation (up two to 18 per cent) and the Greens (down two to 10 per cent).
The firearms legislation will enable a promised gun buyback, which was agreed in a national cabinet deal with the states and territories to tighten gun laws following the attack.
Senator Watt said the Greens only supported the gun reform, leaving the hate speech reform up in the air.
Both bills will be introduced to the House of Representatives on Tuesday morning, when they will be quickly sent to the Senate afterwards.
Fresh figures from the Department of Home Affairs showed there were a record 4.1 million firearms in Australia, more than at the time of the Port Arthur massacre three decades earlier.
One of the gunmen, Sajid Akram, was a licensed holder.
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