(Corrects day of week in second paragraph)
* Top-five shareholder urges Shire to talk to AbbVie
* Other investors write to Shire board pushing case for deal
* Shire yet to respond to AbbVie's latest $51 bln offer
By Anjuli Davies and Ben Hirschler
LONDON, July 11 (Reuters) - Some top investors in Shire are urging it to engage with AbbVie to discuss the U.S. drugmaker's $51 billion takeover bid as a prolonged silence from the London-listed drugmaker adds to uncertainty over a possible deal.
AbbVie, which wants to buy Shire to cut its tax bill and diversify its product line-up, raised its cash-and-stock offer for Shire to 51.15 pounds a share on Tuesday, though this value has since fallen to around 50 as AbbVie shares have slipped.
"Based on the new bid, we think Shire should engage," one top-five Shire shareholder told Reuters on Friday.
Shire shares were 1.2 percent up on the day at 46.55 pounds by 1415 GMT.
Other Shire shareholders have also written to the company's board expressing their support for a deal and have called on Chairwoman Susan Kilsby to open talks with AbbVie's Chairman and CEO Richard Gonzalez, several people with direct knowledge of the situation said.
They argue that 51 pounds is a good enough number for Shire to allow for due diligence, so that the two sides can negotiate a final deal price.
But after rejecting three previous proposals from AbbVie, which it said fundamentally undervalued the company, Shire has still not responded publicly to the latest offer.
Industry sources said the hyperactivity and rare diseases specialist was in constant communication with its shareholders and was weighing their feedback, but it remained unclear which path the Shire board would take.
A number of investors said they believed a deal could be hammered out in a relatively short time - perhaps even over the coming weekend - given Shire has said it is happy for the company to be sold at the right price.
But it is also possible that Shire could yet come out with a strongly worded rejection next week, which would give AbbVie little time to recover. Under British takeover rules AbbVie has until July 18 to announce a firm offer for Shire or walk away for up to six months.
Officials at Shire and AbbVie declined to comment.
CASE FOR INDEPENDENCE
Shire was founded in Britain but is today managed out of Boston, headquartered in Dublin and generates most of its sales in the United States.
Buying Shire would allow AbbVie to join a growing number of companies to move their tax base out of the United States and would give it an effective tax rate of around 13 percent by 2016, against 22 percent last year.
Shire has made a strong case for independence, arguing that its product sales will double to $10 billion by 2020 as it moves into new disease areas.
But many shareholders would rather get rewarded today and are nervous that a deal might slip through their fingers - as happened in May when Pfizer failed in its $118 billion pursuit of AstraZeneca.
AbbVie has also been actively lobbying Shire investors to get their support. The U.S. group said on July 8 that it and its financial adviser J.P. Morgan had met with, or spoken to, investors representing a majority of Shire's shares.
Gonzalez went on to claim that major Shire investors were "generally supportive of this transaction" but was forced to retract this comment under strict British takeover rules because he did not give evidence of such support in writing. (Additional reporting by Olivia Oran and Soyoung Kim in New York; Editing by Elaine Hardcastle)