The high-profile independent Kerryn Phelps remains on track to take the seat of Wentworth from the Liberals after jubilant scenes on Saturday night gave way to a rollercoaster ride in the count on Sunday.

As of Sunday evening, Phelps was more than 1,600 votes ahead of the Liberal candidate, Dave Sharma. Earlier in the day the gap between the two dropped to 884 votes as postal votes strongly favoured Sharma.

But Phelps pulled away again later in the day after adjustments to Saturday night’s count in a couple of large booths. Liberals believe Phelps remains the favourite in the critical contest, although Scott Morrison signalled the result could go for a recount if the margin tightened as the postal votes continued to be logged.

Phelps used television interviews on Sunday to say the Morrison government should run a full term unless there are “exceptional circumstances” rather than be forced to an election as a consequence of losing its majority in the lower house – and she nominated getting children off Nauru as “the first order of business”.

The putative member for Wentworth signalled she wanted quick action about the escalating humanitarian crisis on Nauru. Phelps gave tacit backing to a signal from Scott Morrison last week that resettlement in New Zealand was an option if the parliament passed legislation preventing asylum seekers from ever settling in Australia.

In comments that will add critical momentum to the debate, Phelps said resettling asylum seekers in New Zealand was “an extremely good option” and refugee advocates had spoken to her about that being “a very good interim position, and so it’s definitely on the table”.

Last week, the Victorian Liberal Russell Broadbent – one of a group of Liberals pushing Morrison to evacuate children from offshore immigration detention – made a personal appeal to the Labor leader, Bill Shorten, to support the government’s legislation, declaring people languishing on Nauru need parliament to deliver a breakthrough.

Broadbent wants Morrison to bring on the New Zealand bill this week and test support in the parliament.

Labor also signalled a nascent shift on the issue on Sunday morning. The manager of opposition business, Tony Burke, told the ABC he did not want a repeat of the situation a few years ago where a parliamentary deadlock over transferring asylum seekers to Malaysia scuttled a practical outcome.

Shorten said last week Labor would oppose the government’s bill, because the consequences of it were too far reaching.

But Burke opened the door, suggesting the ball was now in Morrison’s court. “We are yet to find out whether that was just something he was saying in advance of the Wentworth byelection, or whether it’s something he actually believes.”

With internal pressure mounting within the major parties and on the crossbench, Guardian Australia understands the government has quietly removed a number of people from Nauru over the past couple of weeks.

With Sunday’s count after the byelection rebuke to the Liberals seesawing on Sunday, Phelps told supporters she was “holding her breath”.

Holding our breath for the AEC count. This is a white knuckle ride.

Whatever the outcome, I am enormously proud of the work of my volunteers and campaign team. #WentworthVotes — Prof Kerryn Phelps AM (@drkerrynphelps) October 21, 2018

The negative swing against the Liberals on the current count is over 19%. On the two-party preferred measure, Phelps leads Sharma 51.1% to 48.9%.

Morrison told reporters a recount would be triggered if the gap between the two candidates dropped to 100.

The prime minister was contrite on Sunday morning, saying the Liberals needed to heed the lessons of the huge protest vote.

“Yesterday Liberal voters expressed their anger at the parliamentary Liberal party,” he said. “There is no doubt about that. The events of two months ago angered and outraged many Liberals and particularly those in the seat of Wentworth.”

He said the Liberals would respond to the result by positioning in the “sensible centre”. On Nauru, Morrison said he would continue to “work closely with the crossbench members to get the right outcomes there”.

Burke sent a signal that Labor would not rush to move a motion of no-confidence in the government, with federal parliament set to resume for a week-long session on Monday.

Before the Wentworth upset, Morrison had indications of support from the Victorian independent Cathy McGowan and the Queensland crossbencher Bob Katter.

Katter reiterated his support for the government on Saturday night with a long wish-list, including action on drought, regional development and Indigenous health.

The treasurer, Josh Frydenberg, said on Sunday morning the government would continue to seek assurances from the crossbench in order to continue governing over the coming months. He said the message from the byelection result was the Liberal party needed to get on with delivering.

Burke said the government should not seek to hold on, but instead call an election. He said Morrison had spent the Wentworth campaign telling voters a hung parliament would mean political instability and would harm the economy.

“I don’t see how he can argue that and not then say that we have to have an election,” Burke said. “Either Scott Morrison was lying the whole way through the election campaign and he is now going to simply cling to power because, you know, he is the advertising guy and he really just uses whatever argument he wants each day – or we have an election.

“I don’t see there is any middle ground there, given the arguments that both he and his treasurer put about instability in the economy.”

