KKR and Mr Pessina, the firm's leading shareholder and deputy chairman, returned with a new offer or £11.1 billion today, almost five per cent more than the recommended bid it made on Friday.
Hours after Alliance Boots' board recommended Friday's bid, it received a £10.8 billion takeover offer from Terra Firma, the Wellcome Trust and HBOS.
But a statement to the London Stock Exchange this afternoon revealed that the consortium would not be pursuing its interest.
"Boots is a critically important national institution, and we are naturally disappointed not to be able to execute the bold vision we had for the company and its critical role in the provision of healthcare in the UK," the statement said.
"However, we are pleased that the shareholders of Alliance Boots have received a significantly higher price due to our interest, and we wish the company and all its stakeholders well under new ownership."
The bid from KKR and Mr Pessina is 1,139p per share, the same price that its takeover vehicle AB Acquisitions bought almost 50 million shares at last night.
If approved by shareholders, the deal would represent by far the largest acquisition of a UK group by a private equity fund.
Alliance Boots is best known for its high street chemist outlets in Britain, but it also has a sizeable overseas pharmacy presence and wholesale supply business.
Unions have already expressed concerns over workers' futures in light of the private equity bidding war.
Brendan Barber, TUC general secretary, said: "Many such takeovers have hit staff and customers hard as the new owners seek to make the biggest and quickest possible buck at the expense of the long term.
"Staff and customers - including the NHS - need to know whether they plan to invest in Boots, consult with the workforce and honour the terms and conditions already enjoyed by Boots staff, or whether the costs of servicing a debt financed takeover will mean a worse deal."
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