The shareholders of Euronext look set to hold out for higher offers - with management seeing the New York Stock Exchange (NYSE) as the favoured bidder.
Euronext shareholders are facing a crunch decision
A proposal to put Deutsche Boerse in pole position to tie up with the pan-European exchange was rejected at Euronext's annual meeting.
Euronext said that the German group's $11bn (8.6bn euros; £5.8bn) bid was unchanged from one it tabled earlier.
Shareholders felt that both it, and NYSE's $10.3bn offer, were too low.
BBC Europe business reporter Theo Leggett, who was at the meeting, said some shareholders welcomed the prospect of a bidding war.
"Let's not rush into anything, let's wait for a knockout bid. We should be priced at a premium to the market," said one.
Takeover talk dominated the Amsterdam meeting, with Euronext's chief executive officer Jean-Francois Theodore saying that no decision had been made about whether to endorse either bid.
However, shareholders were advised against declaring support for a merger with Deutsche Boerse - with about 59% voting against the move.
Mr Theodore had urged shareholders "not to deprive yourself of your freedom of choice".
Euronext also hinted that the prospect of the German group being investigated by the European Commission for anti-competitiveness in some areas of its business was "a big negative" in deciding which party to merge with.
Deutsche Boerse, which runs the Frankfurt stock market, had described its offer as a "merger of equals".
The German operator said its merger bid would bring about savings worth $380m, although the combined company would be based in Frankfurt - a move that has previously drawn opposition from Euronext.
It also pointed to the $2bn in cash that it was offering shareholders.
Euronext has already indicated that it is attracted to the NYSE offer.
Euronext - which operates the Paris, Amsterdam, Brussels and Lisbon markets as well as the London-based Liffe international derivatives exchange - has been in prolonged talks with Deutsche Boerse over the possibility of a full merger.
But analysts believe Monday's offer from the NYSE, which would create a transatlantic stock market giant worth $21bn, will find more favour with Euronext's board and shareholders.
Still, one key shareholder - The Children's Investment Fund, which owns 10% of Euronext - said it was backing Deutsche Boerse.
Competition between exchanges has been increasing, and a wave of mergers are predicted as companies look to cut costs and boost client numbers.
A rejection of Deutsche Boerse in favour of the NYSE would be a second blow for the German operator, following its unsuccessful attempt last year to take over the London Stock Exchange (LSE).
It would also mark the second time Euronext had spurned its German rival's approaches.
The first time, in 2005, foundered on Deutsche Boerse's insistence on keeping the merged firm's HQ in Frankfurt and taking the leading executive role for its own chief executive.
The LSE has itself been the target of bid interest from Euronext until recently.
But moves by the US Nasdaq exchange - which now has a 25% stake in the LSE - all but blocked Euronext's plans to expand to London.
Under the terms of the proposed NYSE deal, each share in the US operator would be converted into one share of common stock in the merged company, which would be renamed NYSE Euronext.
"This is consistent with our strategic objectives of both expanding geographically into Europe and expanding our product mix into derivatives," said NYSE chief executive John Thain.