But the latest bid was still viewed as falling short of properly valuing AstraZeneca and the company is likely to publicly reject it as early as Monday, according to the Financial Times, which cited people familiar with the matter.
Pfizer wants to create the world's largest drugs company, with a headquarters in New York but a tax base in Britain, where corporate tax rates are lower than in the United States. It has met entrenched opposition from AstraZeneca, as well as many politicians and scientists who fear cuts to jobs and research.
The US group said its new offer was final and could not be increased. It said it would not make a hostile offer directly to AstraZeneca shareholders and would only proceed with an offer with the recommendation of the AstraZeneca board.
Pfizer also increased the cash element in its offer to 45 percent, with AstraZeneca shareholders set to receive 1.747 shares in the enlarged company for each of their AstraZeneca shares and 24.76 pounds in cash.
The new offer represents a 15 percent premium over the current value of a cash-and-share approach made on May 2 - worth 50 pounds a share at the time - which was swiftly rejected by AstraZeneca.
Nonetheless, two analysts - Raghuram Selvaraju of Aegis Capital and ISI Group's Mark Schoenebaum - said they believed the sweetened offer would boost Pfizer's earnings quickly, with Schoenebaum predicting an uplift from 2015.
Pfizer also revealed it had written to AstraZeneca's chairman on May 16 offering 53.50 pounds a share - 40 percent in cash - but had been told that this still substantially undervalued the company, prompting it to make the latest last-ditch offer.
"We believe our proposal is compelling for AstraZeneca's shareholders and that a Pfizer-AstraZeneca combination is in the best interests of all stakeholders," Pfizer Chief Executive Ian Read said in a statement.
He expressed frustration at AstraZeneca's refusal to engage in talks and urged the British company's shareholders to pressure its board to start discussions.
"Following a conversation with AstraZeneca earlier today, we do not believe that the AstraZeneca board is currently prepared to recommend a deal at a reasonable price," Read said. "We remain ready to engage in a meaningful dialogue but time for constructive engagement is running out."
According to the Financial Times, AstraZeneca executives also felt that Pfizer failed to give assurances on other key terms of a deal, including commitments to the UK group's research and development programs.
Two banking sources earlier described 55 pounds a share as the "magic number" at which a deal could get done and Selvaraju of Aegis said Pfizer's declaration that its offer was "final" would concentrate minds at AstraZeneca.
"The main thing that will be likely to get AstraZeneca to engage is that Ian Read, who is a tough guy, has basically said this is our final offer," he said.
In the absence of further discussions or an extension of the deadline for making a firm offer under British takeover rules, Pfizer's proposal will expire at 5 p.m. London time on May 26.
An AstraZeneca spokeswoman said she had no immediate comment on Pfizer's latest proposal, which would see Pfizer shareholders owning 74 percent of the combined company, with AstraZeneca shareholders holding 26 percent.
The increased offer had been widely expected. Pfizer said last week it would consider a higher offer as it urged AstraZeneca's board to enter talks.
DRUG PIPELINE HOPES
The British firm has laid out details of its pipeline of new drugs and argues there is no inevitability about a Pfizer deal, although its management also acknowledges the board would have to consider a compelling bid.
Investors have backed AstraZeneca in rejecting 50 pounds a share, but many have said they would want it to engage in discussions if Pfizer came back with an improved offer. They fear AstraZeneca shares will tumble if Pfizer walks away.
There has been a mounting political backlash against the proposed deal in Britain, the United States and Sweden, where AstraZeneca has half its roots.
The Swedish government launched a concerted effort on Friday against a merger it fears will lead to cuts in science jobs and research, echoing concerns aired by British lawmakers at two parliamentary hearings last week and fears for U.S. jobs in states where AstraZeneca has a large presence.
Pfizer's bid would be the largest foreign takeover of a British firm and is opposed by many scientists and politicians who fear it will undermine Britain's science base.
British Prime Minister David Cameron has said he wants more assurances from Pfizer, and science minister David Willetts said last week he would like to see longer guarantees on investment than the five years currently promised by Pfizer.
The UK government has held exploratory discussions with Brussels about strengthening its ability to force Pfizer to honour commitments on jobs and research under European Union rules.
But Cameron, head of the free-market Conservative Party, has also said Britain does not want to be seen to be pulling up the drawbridge to foreign companies.
Although Pfizer has given a five-year commitment to complete AstraZeneca's new research centre in Cambridge, retain a factory in northern England and put a fifth of its research staff in Britain, it has said this could be adjusted if circumstances change "significantly".
Pfizer's Read said on Sunday: "We stand by our unprecedented commitments to the UK government."
The tax aspects of the deal, meanwhile, have sparked anger in the United States, where lawmakers are now considering legislation to prevent so-called corporate inversions, under which U.S. companies re-incorporate overseas to avoid U.S. taxes.
Inversions have helped fuel a wave of deals in the pharmaceuticals sector in recent months, but buying AstraZeneca would allow Pfizer to carry out the largest such deal yet.