Prime Minister Tony Abbott has raised the prospect of Australia leaving the United Nations refugee convention after a key plank of the government’s border protection plan was scuttled in the Senate.

The Labor opposition and Australian Greens voted in the Senate late on Monday night to overturn temporary protection visas (TPVs) and Mr Abbott has talked of having the parliament sit through Christmas in order to get his legislation passed.

Mr Abbott said the government respected the refugee convention but would have more to say about it in the future.

“We think it’s important that it be dealt with properly and we’ll have more to say on this in the days and weeks ahead,” Mr Abbott said.

The prime minister has previously expressed concerns with the way the convention, which Australia ratified in 1954, had been “imported into Australian law”.

Withdrawing from the convention could damage Australia’s regional and international reputation, especially as it is currently a member of the UN Security Council and is hosting the G20 summit in 2014.

Convention signatories are obliged to give refugees certain rights, such as the right not to be returned to persecution against their will.

The convention also lays down basic minimum standards for the treatment of refugees, including access to courts, primary education and work.

In July, then prime minister Kevin Rudd suggested the convention’s scope needed broadening to bring it into line with modern-day refugee movement.

Mr Abbott, who has been under significant pressure on federal schools funding, described Labor MPs as “wreckers and vandals” who were giving the Australian people a “two-fingered salute” by blocking government bills.

Parliament may sit through Christmas

He threatened to make the House of Representatives sit through Christmas to pass new yet-to-be-revealed laws to make up for the axing of TPVs, as well as to repeal the carbon and mining taxes and raise the debt ceiling to $500 billion.

“I don’t think the Labor party should get a free pass at Christmas time if it’s not prepared to accept that the people voted a certain way,” Mr Abbott said.

Labor’s manager of opposition business Tony Burke said the opposition was unfazed by Mr Abbott’s threat to extend parliament until the end of the year.

“We’re all for it,” he said.

Greens deputy leader Adam Bandt, whose party is in talks with the coalition to find a way of passing the debt ceiling laws, said Mr Abbott needed to take a more constructive approach to all of its bills.

“Tony Abbott needs to understand that it wasn’t just the last parliament that was a minority parliament – this one is, too,” Mr Bandt said.

The Greens may allow the debt ceiling bill to pass the Senate if it is amended to abolish the ceiling altogether and the government agrees to be transparent about what any new debt is for.

Labor and Greens have vowed to block the carbon and mining tax repeal bills, which are aimed at abolishing both taxes from July 1, 2014.

Meanwhile, Opposition Leader Bill Shorten kept Labor’s focus in parliament on schools funding, quizzing Mr Abbott on the details of what the prime minister described as a national agreement with the states and territories.

Asked whether the government would keep Labor’s $1-for-$2 rate of co-contribution with the states, Mr Abbott said: “I am responsible for what the commonwealth does.”

Education Minister Christopher Pyne said the coalition’s deal would make schools more than $1 billion better off over four years, without Labor’s “red tape”.