Microsoft and Yahoo stepped up their takeover talks on Friday night, bringing the last chance for an agreement that might prevent an all-out hostile takeover fight.

The intensification of talks follows a three-month stand-off on price and came amid indications Microsoft was prepared to raise its bid from the original $31 a share it had offered, according to one person close to the situation.

Yahoo’s shares rose 7 per cent on news of the heightened discussions, although at $28.67 they still stood more than $1 below the high point reached in the wake of Microsoft’s initial offer.

In recent days Steve Ballmer, Microsoft’s chief executive, has used the dual threats of turning hostile and walking away from a deal altogether to try to draw Yahoo to the negotiating table.

Yahoo has refused to enter serious talks unless Microsoft first increases its offer.

It was unclear on Friday which side had given ground, although one person close to the situation said Yahoo’s willingness now to engage in talks pointed to an offer worth “significantly more” than the one Microsoft first proposed.

While there have been indirect discussions and informal overtures in recent weeks, the talks on Friday marked the first time Yahoo has been willing to engage in a direct discussion with Microsoft on price, suggesting a breakthrough had been made on the issue the internet company had said was the primary bar to any deal.

However, the person close to the talks cautioned that the two sides were still some way from an agreement and that many factors other than price would also need to be agreed.

For its part, Microsoft executives have said publicly that they stand by their original offer and the company has no need to “bid against itself” to persuade Yahoo to do a deal, though privately the company has signalled there may be room for a slightly higher price in return for an agreement.

In one of the strongest signals yet that he might be prepared to discuss a higher price, Mr Ballmer on Thursday told Microsoft employees in an internal meeting: “I will go to what I think it’s worth if that gets a deal done.”

The value of the cash-and-stock bid has fallen to $29.35 a share since the end of January as Microsoft’s shares have slipped.

To get the value back to $33 a share – the price many on Wall Street have expected Microsoft eventually to pay – the software company would have to add more than 12 per cent to its offer, taking the total value to about $47.5bn.

News of the talks came nearly a week after a Microsoft ultimatum to Yahoo to enter takeover negotiations had expired.

Mr Ballmer had threatened to cut the value of Microsoft’s bid and take the offer directly to the internet company’s shareholders, but his unwillingness to follow through on that threat this week pointed to last-ditch attempts to bring Yahoo to the negotiating table.

A hostile bid could force Yahoo’s board to dig in against Microsoft and add further delay to any eventual deal, according to take-over experts.