Speaking to his Liberal MPs in party room meeting, Abbott promised changes to the way his government operates and asked his colleagues to give him six months to reset the government.
Abbott said he took the result of today's leadership spill motion, which was defeated by 61 – 39, as a "shot across his bow".
According to Australian Broadcasting Corporation, one MP cast an informal vote, merely writing "PASS" on the ballot paper.
Liberal MPs were quoted by ABC as saying that Abbott looked "shocked" when he was shown the numbers.
Abbott asked his team members to have faith in him, telling them that he wanted to fight the Labor Party, not the Liberal Party.
"The Liberal Party has dealt with the spill motion and now this matter is behind us," he said.
"We are absolutely determined to work for you, the people who elected us.
"We want to end the disunity and the uncertainty which destroyed two Labor governments and give you the good government that you deserve.
"We think that when you elect a government, when you elect a prime minister, you deserve to keep that government and that prime minister until you have a chance to change your mind."
Speaking to the media, Abbott said the motion, moved by two West Australian backbenchers, had been a "chastening experience".
"It's not often that something like this happens 16 or 17 months into the life of the government," he told reporters.
"I am confident that as of today we're back at work," said Abbott, who is keen to boost strategic ties with India.

Latest News from World News Desk