Sage said that it was considering trumping the agreed 430p a share cash bid from Solution 6, an Australian group.
It is understood that Bob Morton, City financier and Pegasus' largest shareholder, with a 12.7 per cent holding, is also weighing up a bid for the company after Christmas. Market sources said Mr Morton does not want to sell his stake for less than 500p a share and could use one of his other quoted companies to bid for Pegasus.
Pegasus dismissed the Sage offer, citing concerns it would not get competition clearance.
Sage competes with Pegasus in providing accounting software for small and medium sized enterprises (SMEs). In 1996, Pegasus rejected a 475p a share offer from Sage.
Jonathan Hubbard-Ford, Pegasus chief executive, said: "They [Sage] have never been able to explain to us how they would overcome the competition issues." Mr Hubbard-Ford said, for instance, in the market for modular accounting software for the SME sector, his company held 45 per cent of the market, while Sage had 47 per cent.
However, Paul Stobart, business development director at Sage, said: "[Pegasus'] figures on market share are complete cloud cuckoo land. There's no competition issue at all. With so many new Internet entrants, the market is exploding."
Mr Stobart said yesterday's statement from Sage was intended as a holding position, to dissuade Pegasus shareholders from selling out to Solution 6. He also said that Sage was prepared to table a hostile bid.
Pegasus shares jumped 51p yesterday to 485p, while Sage rose 78p to 769.5p.