The Coalition and Labor have joined forces to vote down a motion to grant amnesty to almost 270 asylum seekers currently in Australia.

Key points: 267 asylum seekers, including 37 babies, have been in Australia pending the High Court decision

267 asylum seekers, including 37 babies, have been in Australia pending the High Court decision A Greens motion to let them stay was defeated 10-40 by the Coalition, Labor, and independent senator John Madigan

A Greens motion to let them stay was defeated 10-40 by the Coalition, Labor, and independent senator John Madigan Immigration Minister Peter Dutton says each case will be examined individually

The 267 people, including 37 babies, are facing the prospect of being sent to Nauru in the wake of yesterday's High Court judgement which upheld offshore immigration detention.

Greens senator Sarah Hanson-Young today moved a motion in the Senate, asking for the Federal Government to allow the asylum seekers to remain onshore.

In full, the motion read: "the Senate calls on the Turnbull Government to grant amnesty to the 267 men, women and children in Australia as part of the M68 High Court challenge, and allow them to stay."

It was defeated 10-40, with independent senator John Madigan siding with the Greens.

Prime Minister Malcolm Turnbull addressed the issue in Question Time, telling the chamber that the Greens did not have the "monopoly on empathy".

Mr Turnbull said that border security measures undertaken by the Government had curbed the numbers of deaths at sea.

"The Honourable Member can share his empathy with us, he can share all of that, but he has to recognise that the approach that his party has advocated... resulted in deaths at sea," he said.

"Women and children, young men, families, that is the consequence of abandoning responsibility at the border."

His comments come amid increasing pressure on Immigration Minister Peter Dutton to allow the asylum seekers to stay onshore.

Mr Dutton has said that each asylum seeker would be looked at on a case-by-case basis, telling the ABC that "exceptional circumstances" would be looked at.

"We are not going to put children into harm's way," he said.

"We are going to work individually through each of the cases."

Mr Dutton said the Government had to be compassionate, but also realistic in its actions following the verdict.

He said he did not want to encourage actions that would lead to more people drowning en route to Australia.

"We are going to continue our vigilance against people smugglers, while providing compassion to those who have been traded in this evil, people smuggling organised criminal syndicate," Mr Dutton said.

"We are acting in the best interests, not only of these children, but children that would follow them. I don't want to reopen the open border policy."