US pharmaceutical group AbbVie has raised its offer for Shire to £51.15 per share, valuing its Dublin-based rival at more than £30bn ($51bn).
Shire responded later that, as the Chicago drugmaker had not sent it the proposal before making the announcement, its board would meet to consider the proposal.
"Shareholders are strongly advised to take no action in relation to the AbbVie proposal," it urged.
Analysts predicted the board would reject the offer, leading some to predict the takeover could become hostile, with AbbVie having said it had made the new offer after speaking to Shire shareholders "representing a majority of Shire's outstanding shares".
The £51.15p per share proposal, which is made up of £22.44 in cash and 0.8568 ordinary shares
of the combined group for each Shire share, is an increase of roughly 11% or £3bn on AbbVie's previous offer.
Shire, which moved it corporate domicile to Ireland in 2008, has already rejected three bids from AbbVie, saying it not only thought the offers fundamentally undervalued the business's prospects but also stated concerns about the execution risks of its "inversion" plans to cut its tax bill by redomiciling to Britain.
On Tuesday AbbVie said its new proposal was an increase of £2.00 and approximately 10% in cash per Shire share, and was a premium of 75% to Shire's closing share price of £29.25 on April 17th, the date before its first bid.
Analysts had been predicting an even higher offer, with Jefferies recently anticipating a $55bn bid.
AbbVie's Chairman and Chief Executive Officer Richard Gonzalez reiterated his belief that the combination would create a strong company with a "compelling investment thesis" thanks to the US company's greater financial strength and research experience.
"AbbVie has made a compelling offer to Shire that creates immediate and long-term value to shareholders of both companies. We think its shareholders should strongly encourage the Shire board to engage in constructive dialogue with AbbVie."
Under UK takeover rules, a "Put Up or Shut Up" deadline gives AbbVie until July 18th to have a bid accepted.
AbbVie added that it was "willing to move quickly and cooperatively to engage with Shire with a view to achieving a transaction for the benefit of all shareholders".
Analyst Savvas Neophytou at Panmure Gordon suggested that the board would reject this offer but if AbbVie went hostile they might not face the same level of political opposition as Pfizer did for its AstraZeneca bid.
"It's big share price move, more than Kraft's revised offer for Cadbury, but ultimately it's designed to increase pressure on Shire's management to engage, with a view to settling on a recommended offer, which we would imagine will be greater than £51.15 but not higher than £55.
"Unless AbbVie decides to go hostile, which is a distinct possibility, because Shire does not have the same level of support as AstraZeneca did. One issue focuses the mind; this transaction brings Shire back to a UK domicile, which should boost the tax revenues for the UK and investment in R&D as a whole, which politicians will embrace in my view."
Analyst Richard Purkiss at Atlantic Equities agreed that it was not quite "a knock-out offer".
Shares in Shire spiked from 4,576p to 4,751p on the announcement, but retreated to 4,483p by 15:40, a fall of 3.6%.