But by Sunday evening, his candidate trailed an independent rival by 1,600 votes with several thousand votes still to be counted, the Australian Electoral Commission (AEC) said.
It could be some days before the uncertainty is cleared as postal votes received within 13 days after the ballot are still counted.
"I'm not sure we have an understanding of what is the vision of the Prime Minister and his team", she said, pointing to the chaos of last week.
Despite heading towards a minority government, Mr Morrison has talked up the coalition's relationship with the crossbenchers.
Morrison said if the vote gets as close as 100 votes an automatic recount would be triggered, giving his conservative coalition a slender chance of retaining its one seat majority in parliament. "I hope the government will knuckle down and deliver good governance". "But I respect them for doing so and they make a great contribution to Australia".
Michelle Grattan, a political commentator, said a Liberal loss would be a "devastating blow for the Prime Minister".
Sharma grabbed the lion's share of 5,463 postal votes counted this morning, 57% of the primary votes to Phelps' 17%, and almost 65% on a two-party preferred basis to slash the independent's lead to just 884 votes.
If the win for Dr Phelps is confirmed, the coalition government will be forced to rule as a minority in the Australian Parliament.
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But the government said it would only do so if those people were then banned from ever entering Australia again under any circumstances.
Earlier in the program, Phelps reiterated her belief that governments should "serve their full terms".
While the government now has pledges of confidence from some crossbenchers, they would be in a strong position to demand concessions in a hung parliament. "Many people are angry and they expressed that today", Morrison said.
I mean, there was a lot of anger about the way Malcolm Turnbull was treated, ' she said.
On a two-candidate basis Phelps is now leading the Liberals Dave Sharma 51.1% to 48.9%.
"We have been at 75 (seats), not 76, since the former prime minister resigned", Mr Morrison told reporters.
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.
Australian Medical Association representative Dr Paul Bauert, who has treated patients on Nauru, said the "sad" situation was dire and urgent.
Sharkie, who had guaranteed the government confidence until after the byelection, said she wanted to hear how Morrison was going to deal with the children on Nauru. The issues of climate change, asylum seekers, LGBTQI rights and the argument over gambling ads on the Opera House are likely much more important for its affluent, socially progressive voters than in other marginal seats that will decide the federal election.