The US firm’s latest bid for Sky is an increase from the £12.50-a-share offer it put forward earlier this year.
It was also higher than the £14-a-share offer put forward by Rupert Murdoch’s 21st Century Fox.
Brian Roberts, chief executive of Comcast, said: “We have long admired Sky which we believe is an outstanding company and a great fit with Comcast.
“Today’s announcement further underscores this belief and our commitment to owning Sky.”
On Wednesday, Fox and Sky announced they had reached agreement on the terms of a new offer of £14 per share, valuing Sky at £24.5bn.
Comcast’s new bid translates 18 per cent more than its original offer.
The duel for Sky is unfolding as Fox itself is the object of a takeover battle between Comcast and Disney.
Disney said in June it was offering more than $71bn (£54bn) for Fox’s entertainment businesses in a counterbid to Comcast’s nearly $66bn offer.
Sky operates in Austria, Germany, Ireland and Italy as well as the UK. It has 22.5 million customers, attracted by offerings such as the English Premier League and Game of Thrones.
Fox, which is run by media mogul Rupert Murdoch, still faces significant regulatory battles in Britain.
The challenges include the culture secretary’s assertion that Fox would have to sell Sky News to win government approval because of concerns about media plurality.
Fox’s bid for Sky is the most recent episode in Mr Murdoch’s long-running effort to take full control of the company.
Additional reporting by agencies