"There are still many postal votes to be counted", Mr Morrison said in Sydney.
Addressing the prospect that his government would lose Wentworth, Morrison rejected calls for an early election from the opposition Labor Party.
The by-election was triggered by the resignation of the seat's sitting member of parliament-former prime minister Malcolm Turnbull.
This morning, Dr Phelps revealed her campaign cost around $300,000. But with a quarter of the ballots still to be counted on Sunday the Liberal candidate was just 900 votes behind.
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.
The defeat will intensify soul-searching within the Liberal Party, with member for Reid, Craig Laundy, predicting those who played key roles in the leadership spill would begin to blame Mr Turnbull.
She said running in the by-election was the "farthest thing from my mind" until Mr Turnbull was dumped as prime minister.
The latest Australian Electoral Commission figures published at 3.30pm on Monday show Dr Phelps on 51.06 per cent of the two-candidate preferred vote with a lead of 1559 votes.
Labor did not capitalise on the Liberal Party vote collapse: one hour after polls closed, the Greens' Dominic Wy Kanak was besting the opposition party's Tim Murray on the primary vote.
If Phelps is confirmed the victor, she will join the cross bench, leaving Labor with 69 seats and the Coalition with 75 - one short of a majority.
However, the Wentworth frontrunner insisted she was a safe pair of hands and believed the Government should run its full term, even though there was "momentum for change".
According to her website, Phelps wants to ensure governments don't keep tinkering with the rules around super.
"What we have done is tapped into a sentiment in the Australian people, to talk about the issues that are important to them, not the issues about survival for a particular political party", Phelps told supporters during her victory speech.
"Everywhere I went in the streets in the eastern suburbs, somebody would come up to me and say, 'Would you please have a run at Wentworth?'", Dr Phelps told ABC TV on Sunday.
"I think there are moves afoot to find a solution particularly for the children and their families to bring them to Australia. and the Australian people are saying loud and clear we want a solution and we want those people brought to Australia".
Sharkie said: "I don't want to hold the government to ransom but I want to hold them to account".
Independent Andrew Wilkie will not guarantee confidence, while Greens MP Mr Bandt said an election had to be called because "the sooner we turf out this rotten government, the better". A large chunk of this is likely to be the disappearance of Malcolm Turnbull's personal vote, but if the swing is just partially replicated in a general election the Liberals are going to be obliterated.