Monsanto has rejected a $62bn (£43bn) offer from Bayer that would have created the world's biggest agricultural supplier.
The US company said the offer was "financially inadequate", but left the door open for a potentially higher bid.
Hugh Grant, Monsanto chief executive, said the proposal significantly undervalued the company.
He also raised concerns about whether a deal would be approved by regulators.
Monsanto shares rose 3.1% to $109.30 in late trading in New York, while Bayer rose 3.2% to €87.15 in Frankfurt.
Bayer called its bid an "extraordinary opportunity to create a global agriculture leader".
The German group offered $122 a share in cash, making it the largest all-cash offer, according to Thomson Reuters data - just pipping InBev's $60.4bn offer for Anheuser-Busch in June 2008.
It was not clear what price Monsanto would accept, but analysts have suggested that Bayer would have to pay significantly more to secure a deal.
JPMorgan analysts wrote: "We believe it is unlikely that the deal gets done at $122 and still believe $135 is a more likely price."
The deal comes amid considerable consolidation in the agricultural sector.
ChemChina plans to buy Syngenta for $43bn after the Swiss-based company rejected a bid from Monsanto, while Dow Chemical and DuPont are forming a $130bn business.
With German rival BASF having previously considered a deal with Monsanto, Bayer is attempting not to be left behind.
A merged Monsanto/Bayer would have a commanding position in markets including the US, Europe and Asia.