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.
Smith said Australia and Indonesia had 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.
He said 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.
Canberra is also continuing attempts to get another boatload of about 255 Sri Lankans, moored at the Indonesian port of Merak, to disembark.
Smith said Australia was reaching out to bilateral and international partners to curb people smugglers.
"This issue can only be dealt with through cooperation between source country and destination country," Smith said.
"Sri Lanka will cooperate with Australia to investi