Opposition Leader Tony Abbott says the prime minister will need to take the first step if she wants to talk to the coalition about backing migration law changes.
The government next week will bring to parliament changes to migration and child guardianship laws to restore power to the executive after the High Court quashed the Malaysia agreement.
Under the agreement, Australia was to send 800 people who arrive by boat to Malaysia in exchange for 4000 properly processed refugees, in a bid to send a tough signal to people smugglers.
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With the Greens standing firm against the changes, Labor will need the coalition's support to get the changes through parliament.
Mr Abbott told reporters in Queanbeyan on Thursday the prime minister would need to take the first step if she wanted to meet with him to discuss a compromise.
"That is up to her," he said.
"She is normally pretty vituperative when we have our daily meeting in question time."
Mr Abbott said he was not complaining.
"That's her style, but our duty is to support the national interest.
"And we believe that the national interest is best secured by stopping that boats through (reopening processing on) Nauru, temporary protection visas and turning the boats around where it is safe to do so."
The Malaysian swap agreement was a "proven failure", with 1000 people arriving by boat since it was announced and 400 since it was formally signed.
"If the prime minister wants to put good policy in place she will get support from the coalition," Mr Abbott said.
The opposition leader will be briefed on the law changes by the solicitor-general and other government legal officers in Melbourne on Friday.
GREENS TO BE BRIEFED ON CHANGES
The Australian Greens have agreed to be briefed by immigration department officials on proposed changes to migration laws, but say there is no chance they will change their tune on supporting the amendments.
Greens immigration spokeswoman Sarah Hanson-Young says she and leader Bob Brown will meet immigration officials on Thursday afternoon.
"We'll be putting to the department very squarely that we want the evidence basis of the claims that were made in relation toonshore processing of asylum seekers," she told reporters in Canberra.
"We'll be asking them ... what evidence they have that offshore processing actually acts as a deterrent ... and what we can be doing more to support people to have safe pathways to Australia."
Senator Hanson-Young said the Greens would not support the law changes, or any proposed amendments by the coalition.
Coalition figures have indicated a possible amendment that would ensure Australia only sends asylum seekers to be processed in countries that have signed the UN refugee convention.
"We will be opposing it at every stage," Senator Hanson-Young said.
The Greens also will question the officials on claims, made in a briefing to reporters last week, that more onshore processing could lead to social unrest.
"It's irresponsible to promote fear, to promote hatred," Senator Hanson-Young said.
Meanwhile, Labor backbencher Graham Perrett said he was not confident the coalition would back the amendments.
"I would not bet my house on Tony Abbott on being bipartisan," he told reporters.
But he said it was "illogical" for the opposition leader to reject the amendments, as offshore processing was the goal of both major parties.
"So one would have thought you could come up with process that let the government of the day to pursue its goal," he said.
