"The support that you have given this campaign and I know this isn't a victory for one person, this is a victory for a community of people who wanted to see politics done differently".
ABC election analyst Antony Green says the Wentworth by-election result is "much narrower" than he expected but he still favours independent candidate Kerryn Phelps to win the seat from the Liberals.
The seat was previously held by Malcolm Turnbull, the former prime minister who was ousted by his party in August and subsequently resigned.
If Dr Phelps does claim the seat, then the Opposition would still need an absolute majority of 76 votes to throw out the Government's agenda in the House - which means one Government MP would still need to cross the floor.
Phelps, a former leader of the nation's peak medical professional body, has also said she won't support a vote of no-confidence in the government.
At the heart of voter discontent in the traditional Liberal seat, which was held by Turnbull by an 18% margin, was widespread frustration about the leadership merry-go-round and constant infighting in Canberra.
Dr Phelps said she would set two priorities: action on climate change and getting asylum seeker children off Nauru. "I would reject bad legislation".
"We will simply wait for that normal democratic, robust and credible process to follow it's course", Mr Morrison said.
The ABC reports, with almost 40 per cent of the votes counted, Liberal candidate Dave Sharma had won only 38 per cent of first preferences, while Dr Phelps won 33.
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"Just a few short weeks ago I was told this was an impossible task and if we actually managed to win the seat of Wentworth, that it would be a miracle", Phelps said in her victory speech.
"This is the beginning of the end of the Morrison Government", he told supporters on Saturday night.
Independent Bob Katter said he did not want to see the government destabilised or an early election called.
"Liberals are angry and they've expressed that", Morrison said.
Meanwhile, Treasurer Josh Frydenberg says the government will continue to seek assurances from crossbenchers to hold off the threat of an early election.
However he appeared unfazed about having to negotiate a minority parliament, as Julia Gillard was forced to after the 2010 election.
Fellow independent Andrew Wilkie said he would not guarantee confidence or supply, while fellow crossbencher Cathy McGowan declined to comment.
'There has been high expectations that this is a seat that can not be lost by the Liberal Party - I have never thought that'.
But this morning Green said four large pre-poll voting centres with 18,000 votes had been released close to midnight, narrowing the vote.