The number of boat people arriving in Australia last year surpassed the amount budgeted by the Immigration Department.
Department secretary Martin Bowles told a Senate estimates hearing in Canberra that "around 12,000" asylum seekers had arrived by boat already.
AAP reports the exact number was 12,884 people. The federal government budgeted for 12,000 for the 12 months to June 30, Mr Bowles said on Monday - just before an announcement that another boat had been intercepted off the Ashmore Islands with 53 passengers and two crew on board.
In the committee hearing, Senator Michaelia Cash inquired whether more were expected to arrive.
"So, no one else is going to arrive from now and the end of June - is that the prediction?" she asked.
Senator Cash pointed to figures released as part of the estimates process that showed costs for dealing with asylum seekers had more than doubled this financial year, from $A1.1 billion forecast in the budget last May.
Mr Bowles conceded the expected costs might be revised, but said they did not depend only on the numbers arriving.
He said the department is changing the way it processes asylum seekers and moving more people out of detention.
AAP reports the government expects costs relating to its asylum-seeker policy to fall from $A2.23 billion in 2012/13 to about $A340 million in 2015/16.
Mr Bowles earlier admitted Malaysia had not yet agreed to strengthening human rights protections for asylum seekers under a people-swap deal between the two nations.
The two countries have discussed a deal since an expert panel recommended last August that Malaysia provide more protections for minors, but no changes to the agreement have yet been made.
The ABC reports 415 asylum seekers are currently being held on Nauru and a further 274 in Papua New Guinea. Eventually, the Nauru centre is expected to accommodate 900.