The London Stock Exchange (LSE) has rejected US firm Nasdaq's £2.7bn takeover bid, saying it "substantially undervalues" the company.
LSE also turned down Nasdaq's request for a meeting after the market operator made a second bid for the firm and upped its stake in LSE to 28.75%.
Nasdaq was "disappointed" by the LSE's decision but said the offer was "full, final and fair" to shareholders.
The government said it was neutral as to the nationality of LSE's owner.
Shares in the London stock market company have surged more than 124% over the past year amid ongoing speculation it will be subject to a takeover offer.
Its shares rose a further 6% on Monday on news of Nasdaq's bid and maintained the gain by closing.
At the moment LSE shares are trading well above the offer price at £12.91 per share - well above Nasdaq's bid of £12.43 - suggesting that investors still want a higher premium before the takeover will be accepted.
Nasdaq said it planned a dual listing in London and New York if its bid, the second it has made for LSE, was successful.
LSE BID TIMELINE
December 2004 - Deutsche Boerse tables £1.35bn offer
December 2004 - Euronext makes merger approach
March 2005 - Deutsche Boerse drops takeover plans
December 2005 - Macquarie tables £1.5bn bid
February 2006 - Macquarie ditches offer
March 2006 - Nasdaq tables £2.4bn bid
March 2006 - Nasdaq withdraws bid, Deutsche Boerse drops plans for LSE offer
April 2006 - LSE denies reports of an approach from New York Stock Exchange
May 2006 - Nasdaq raises LSE stake to 25.1%
September 2006 - Brokerage Icap calls off merger talks
November 2006 - Nasdaq tables "final offer" of £2.7bn, ups stake to 28.75%
But LSE said the offer failed to reflect LSE's strong financial and strategic position.
"We believe Nasdaq's final offer fails to recognise the outstanding growth record and prospects of our group on a standalone basis let alone the Exchange's unique global position," chief executive Ms Furse said.
Nasdaq said it would not be revising its "final offer" unless another company decided to make a bid for the London market.
"We are excited about the prospect of combining two strong businesses to form the leading global, cross-border equity market platform giving issuers the ability to dual-list simultaneously in London and New York," said Nasdaq president and chief executive Robert Greifeld.
"This is a long game that we're playing, and I'm optimistic we'll engage with the London Stock Exchange board in a relatively short period of time," he added.
BBC Business Editor Robert Peston said it was almost inevitable that the LSE would reject the offer.
"The LSE is bound to reject this offer, it will say the business is growing fast and that Nasdaq is being opportunistic," Mr Peston said.
He added the London exchange could have a hard time seeing off the approach as the Nasdaq now held a significant stake in the firm while there was "almost no basis for the UK authorities to block this deal".
He added that the Nasdaq had swooped now to take advantage of a recent fall in the LSE's share price which came in the wake of news that seven investment banks were creating a rival to the LSE.
In March, Nasdaq dropped a proposed £2.43bn ($4.2bn) bid for the exchange after the LSE rejected its advance.
The US firm is the latest in a long line of foreign suitors to approach the London market.
German market Deutsche Boerse, Australian investment bank Macquarie and the pan-European exchange Euronext have all abandoned offers for LSE since December 2004.
The approaches have prompted the UK watchdog to voice concern about a foreign takeover as it could lead to regulatory changes.
Nasdaq attempted to ease these concerns saying the UK exchange would continue to be regulated solely by the UK's Financial Services Authority.
The government said it was concerned not with the nationality of LSE's owner but that its current regulatory regime was safeguarded.
"The UK has for some years been open to overseas investment in UK exchanges," said Ed Balls, Economic Secretary to the Treasury.
The LSE has resisted approaches saying it can continue to grow alone.
But analysts and market observers have speculated that the Nasdaq is in a strong position and stock exchanges will need to merge if they want to keep on growing and offer a wide-range of global financial services.
Last month, City leaders warned that the LSE risked losing its dominant market position in the face of growing global competition.