The Australian Government's problems with asylum seekers continue to mount, with protests continuing, a further rejection by East Timor of a regional detention proposal, and pressure building from all sides.

Yesterday, protesters climbed on to the roof of Immigration Minister Chris Bowen's Sydney office, joining detainees still refusing to come down from their vigil at the city's Villawood detention centre.

Other protests, including self-harm, violence and hunger strikes, have been held at facilities on Christmas Island and in Western Australia.

The issue has become a political nightmare for Prime Minister Julia Gillard's minority Labor Government, now facing anger from its own left as well as bitter opposition to its policies from refugee advocates and the Opposition.

In the past two years the number of people in detention centres has soared from fewer than 500 to almost 7000, with large numbers intercepted at sea as they neared Australia from Indonesia,

Yesterday, the Government tried to reinforce its claims of effective control of its maritime approaches, with new figures released by Home Affairs Minister Brendan O'Connor showing a plunge in illegal foreign fishing, from 360 vessels apprehended in 2005-2006, to 11 since June last year.

But the numbers of boats carrying asylum seekers intercepted off Australia continues to climb, opening the Government to claims by the Opposition that it has lost control of the nation's borders.

Gillard's proposed answer - a regional detention facility in East Timor - increasingly appears dead in the water.

Rejected by the Left and refugee advocates as a return to a conservative now-defunct "Pacific solution" of centres in Papua New Guinea and Nauru, the proposal has struggled to gain credibility from the outset.

Yesterday the Sydney Morning Herald, quoting an interview in Dili's Independente newspaper, said East Timorese President Jose Ramos-Horta had publicly rejected the plan.

Ramos Horta was previously the only senior political figure still open to the proposal.

"Timor-Leste [East Timor] says that we will not agree to set up an asylum-seeker processing centre in the country," Ramos-Horta said.

Officially, the Australian Government maintains that East Timor's Council of Ministers is still considering Gillard's plan, but Ramos-Horta appears to have closed the door.

"There should be a regional agreement and the agreement should not be made by Timor-Leste and Australia because it is not a bilateral problem," he said.

Gillard is having further problems with the Government's decision to toughen laws against detainees who use violence or commit other crimes while their cases are being decided.

The proposed changes would enable the Government to deport detainees convicted of crimes in detention or refuse permanent protection visas and instead issue the more limited temporary visas introduced by the former Howard Government and dropped by Labor when it came to power in 2007.

The new laws have also been attacked from one side by the Labor left and refugee and human rights groups, and from the other by conservative politicians.

Opposition Leader Tony Abbott has also called for tougher action against asylum seekers who in the past few months have rioted and burned facilities at Christmas Island and Villawood, and who yesterday were continuing rooftop protests.

Federal authorities have held back from violent confrontation at Villawood, and New South Wales police have not been able to act because the centre is a federal facility.

But Bowen said he could not interfere in operational decisions made by federal and detention centre officials.

"I'm not going to say to people like the Australian Federal Police and Serco, I want you to get up on the roof, have an altercation with them and get them down," he said.