Australian Prime Minister Kevin Rudd and new Immigration Minister Tony Burke have conceded Labor has been too slow to act on asylum seeker boat arrivals in the past.
Mr Rudd dismantled the Howard government's Pacific Solution policy when he came to first office.
The Opposition says that decision is to blame for creating conditions for thousands of asylum seekers to try and reach Australia by boat.
Mr Rudd told the ABC on Wednesday that Labor had a mandate to dismantle offshore processing in 2007 and honoured the commitment.
"If we have made a mistake, let me just say this," he said. "It was in perhaps not being quick enough to respond to the new change in external circumstances with an outflow from Sri Lanka from a civil war in 2009-10."
The Gillard government reintroduced offshore processing in Nauru and on Manus Island in 2012.
The ABC reports Mr Burke, the new immigration minister, railed against offshore processing during the Howard era.
In 2006 he said the last thing Australia should be doing was dumping desperate people in Nauru.
But in his first interview since taking on the immigration portfolio, Mr Burke told the Lateline programme on the ABC his opposition to offshore processing at that time was wrong.
"I had a view which was wrong, which was that you could choose settings, keep them in place and they would deal with all of the changes in international situations," he said.
"The view that we should never do (offshore processing) turned out to be wrong."
He said Labor should have changed its policy faster in response to unrest in nations like Sri Lanka, Afghanistan and Iraq.
"We missed the mark by not changing as quickly as we needed to when international situations changed," Mr Burke said.