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The vote results, announced at 1830 GMT, gave Mrs Thatcher 204 of the 372 votes against 152 for Mr Heseltine, leaving the prime minister four votes short of the 56 majority required. Sixteen MPs abstained.
The contest now goes to a second round, seriously undermining the prime minister's authority within her own party.
There was pandemonium among Conservative MPs huddled outside the committee room in Westminster to hear the news.
Thatcher supporters reacted with anger that the contest would be prolonged by another week, and strongly criticised the leadership system which allowed the challenge in the first place.
Mr Heseltine's supporters were confident he could pick up enough votes on the second ballot to win.
The leadership contest was triggered by the devastating resignation speech last week of the Deputy Prime Minister, Sir Geoffrey Howe, in which he was highly critical of Mrs Thatcher's methods.
Mrs Thatcher will now face intense pressure to stand down when she returns tomorrow from the European security summit in Paris.
However, within minutes of hearing the result, she addressed reporters and photographers on the steps of the British Embassy to say it was her intention to fight on.
"I am naturally very pleased that I got more than half the parliamentary party and disappointed that it's not quite enough to win on the first ballot. So I confirm that it is my intention to let my name go forward for the second ballot," she said.
Mr Heseltine expressed gratitude for a formidable vote and said he too would press on, ignoring rightwing appeals to him to stand down.
The Labour opposition leader, Neil Kinnock, has tabled a motion of no confidence in the government and called for an immediate general election.
The Liberal Democrat leader, Paddy Ashdown, said Mrs Thatcher should resign.
It's thought Mr Heseltine's commitment to a review of the deeply unpopular poll tax swung many voters away from Mrs Thatcher.
Senior Tory MPs were speculating openly that the Chancellor, John Major, would emerge as a strong candidate for the leadership if Mrs Thatcher were to step down.
Margaret Thatcher resigned as leader of the Conservative Party two days later after advice from her Cabinet, bringing to an end more than 11 years as prime minister.
Chancellor John Major and Foreign Secretary Douglas Hurd joined the next stage of the leadership contest.
John Major won by a clear margin, and became prime minister five days after Mrs Thatcher's resignation.
The Iron Lady remained MP for Finchley until 1992, but even after leaving Westminster she continued to be a formidable force in British politics.
Her appearances at Conservative Party conferences overshadowed successive Tory leaders years after her resignation, and she frequently spoke out to lend her support to the Euro sceptics.
Ill health forced Mrs Thatcher to abandon many of her public engagements in 2002.
Michael Heseltine returned to government as Environment Secretary under John Major, with particular responsibility for abolishing the poll tax.
Later he served as deputy prime minister, but he never realised his dream of leading the party.
He stood down as an MP in 2001 and was given a life peerage.
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