Immigration Minister Scott Morrison has played down the effects of Australia's degraded relationship with Indonesia on the government's border protection policy.

Mr Morrison confirmed to reporters in Sydney on Friday that Operation Sovereign Borders was continuing, despite Indonesia's anger over the phone-tapping issue.

"Operation Sovereign Borders ... is designed to ensure the operation stands or falls on no single measure," he said.

"We have the ability to work through our chain of measures to ensure that whatever circumstances we face ... we are able to adapt and ensure the people smugglers will be frustrated."

The issues between Prime Minister Tony Abbott and President Susilo Bambang Yudhoyono were being addressed by them personally and he would not comment further.

"I don't think that is in our national interest," Mr Morrison said.

Operation Sovereign borders chief, Lieutenant General Angus Campbell, also refused to comment on the effect of the phone-tapping allegations on Australia's border protection policies.

A senior ranking source from the Indonesian National Police anti-people smuggling taskforce said the asylum-seeker issue remained highly sensitive.

"It's too sensitive to talk about," he told AAP.

Australia's efforts to smash the people smuggling rings is an "end to end" process taking in source countries such as Malaysia and Pakistan, and not just Indonesia, Mr Morrison said.

Up to 60 per cent of asylum seekers trying to get to Australia come via Malaysia, the minister said.

He said he believed Indonesia would continue to be "good international citizens and good regional partners."

At the press conference Mr Morrison would not confirm if he ordered an asylum seeker vessel to be towed when it broke apart about 20km from Christmas Island.

The vessel, carrying 35 people and four crew, was intercepted on Sunday.

So far in November, four boats carrying 198 people have been intercepted, down from 43 boats in the same period the year before.

However he said he expects people-smugglers to "try things on" this month, the traditionally busy pre-monsoon period.

Mr Morrison also blamed a backlog of unaccompanied minors in detention centres on the previous Labor government.

There were 719 unaccompanied minors awaiting assessment in offshore and onshore centres and in community placement.

Media reports this week said a 15-year-old unaccompanied girl was flown to Nauru earlier this week.

"Thirty-three thousand people were left behind by the previous government," Mr Morrison said.

"That, I think, is an abhorrent way for a government to walk away from its responsibilities and we are now working through that legacy caseload, including those unaccompanied minors."

Asked what he was doing to ensure the childrens' health and safety, the minister said: "We have contracted relations with those who directly provide services to unaccompanied minors."

Opposition immigration spokesman Richard Marles said Mr Morrison was spending more time hiding secrets than doing his job.

"Scott Morrison won't answer questions in parliament, he won't answer questions at press conferences," he said in a press statement.

"This is no longer a weekly briefing - it's a weekly embarrassment for Scott Morrison."

Meanwhile, the Greens will move a motion in the Senate to recall Immigration Department officials and Lt. Gen. Campbell before the Legal and Constitutional Affairs Committee.

"I have written to members of the Labor Party urging them to support the Greens move to recall the committee," Senator Hanson-Young said.