US drugmaker AbbVie has raised its offer for London-based pharmaceutical producer Shire to £30.1 billion ($51.3 billion), hoping to win over its reluctant target after three earlier offers were rejected.

The latest £51.15 per share cash-and-stock offer is 11% higher than AbbVie's previous proposal of £46.26, which the UK hyperactivity and rare diseases specialist had said fundamentally undervalued the company.

Industry analysts were sceptical as to whether this was enough to get a deal done, but said the sweetened offer improved AbbVie's chances of getting Shire into discussions.

Shire said its board would meet to consider the higher offer, which it claimed it did not receive before it was announced to the market.

AbbVie is eager to buy the British company, both to reduce its tax bill by moving its tax base to the UK - a tactic known as inversion - and to diversify its drug portfolio. It currently receives nearly 60% of its revenue from rheumatoid arthritis drug Humira, the world's top-selling medicine, which is due to lose US patent protection in late 2016.

The US firm's CEO, Richard Gonzalez, has pressed the case for his pursuit of Shire in a series of meetings with shareholders on both sides of the Atlantic, after setting out the strategic rationale for a deal on June 25.

AbbVie said it and its financial adviser J.P. Morgan had now met with or spoken to Shire investors who represented a majority of the UK company's shares.

"I believe they are generally supportive of this transaction and I can tell you that this offer is responsive to the feedback we have received," Gonzalez told the news agency Reuters.

While refusing to be drawn on the possibility of increasing his offer further, he said he was not aware of any rival counter-bidder but did not rule out a hostile move if Shire failed to engage.

The hustle is the second attempt by a US drugmaker to buy a London-listed rival after Pfizer's $118 billion pursuit of AstraZeneca - another deal driven in large part by tax savings - failed in June.

AbbVie said the new offer reflected a substantial sharing of potential synergies between shareholders of each firm, adding that Shire shareholders would own 24% of the enlarged group.

Under British takeover rules, AbbVie has until July 18 to announce a firm offer for Shire or walk away.

While founded in Britain, Shire today has a minimal business footprint in the country. It is managed from Boston, headquartered in Dublin and has most of its sales in the US. As a result, the potential takeover of the company has not created the political storm that accompanied Pfizer's pursuit of AstraZeneca.