A poll published in The Australian newspaper on Monday indicated that the asylum-seeker issue had damaged Rudd's standing, with 53 per cent of respondents saying he was doing a bad job on the policy and 46 per cent saying his approach was too soft.
Only 16 per cent of respondents said he was too tough on the issue while 29 per cent agreed with his handling of the situation.
A separate Nielsen poll on Monday, published in The Age and Sydney Morning Herald newspapers, indicated Rudd's disapproval rating was up five points in a month to 28 per cent and 44 per cent of Australians thought his asylum-seeker policy was too soft.
Nielsen pollster John Stirton said "approval of Mr Rudd's handling of the asylum-seeker issue is 23 points lower than his overall approval as prime minister", but added that it was only "a small negative" for the government.
"He still has one of the highest prime ministerial approval ratings that we have seen," Stirton pointed out.
The asylum-seeker issue reached crisis point last week after a boat carrying 39 Sri Lankans sank off the Cocos Islands, drowning a suspected 12 asylum-seekers.
Seventy-eight Sri Lankans were rescued from a sinking boat in Indonesian waters last month. They have insisted on remaining on the Australian customs ship that picked them up, refusing to disembark in Indonesia.
Australia and Indonesia have ruled out the use of force to remove the Sri Lankans from the ship, and both nations are keen to resolve the standoff by the end of the week.
The two countries were close to finalising a deal to end the standoff, with Australia offering to fast-track resettlement for those who were found to be genuine refugees, according to the Australian Broadcasting Corp.
Canberra is also continuing attempts to get another boatload of about 255 Sri Lankans moored at the Indonesian port of Merak, to disembark.
Rudd says the surge of asylum-seekers is a result of internal factors in war-torn Sri Lanka and Afghanistan, not any softening of Australia's immigration policies.