The share price jumped from pounds 15 to pounds 16.50, valuing the company at pounds 179.6m, against pounds 129.0m on Thursday, the day before Johnston announced its offer.
Johnston, which has already bought 14.99 per cent of the group, is offering pounds 16 a share to take its stake up to 24.99 per cent. On Friday it requested DTI consent to allow it to raise its stake beyond this.
Charles Brims, chief executive of Portsmouth, yesterday held the door open to a higher bid from a rival group or venture capital company, saying all offers would be considered.
"We are not being a dog in the manger about this. If someone comes up with a higher offer we will look at it. But if we are going to sell, it will be at a much higher price than pounds 16 a share."
Mr Brims declined to discuss details of negotiations. Likely bidders include Newsquest, the rival news company, and Trinity, the media group which recently made an unsuccessful offer for the Mirror Group.
Three of Portsmouth's biggest shareholders yesterday took the opportunity to take profits. Shares in the group have sharply underperformed the FT All-Share index for most of the last five years.
Phillips & Drew sold more than half of its stake and hung on to 5.2 per cent, while Aberforth reduced its holding from 5.4 to 2.3 per cent. Mercury Asset Management also sold more than half its stake, leaving it with 2.3 per cent.
The outcome of the battle now lies in the hands of two families, the Storeys and the Cators, who, together with associates and directors, own 40 per cent of the group. Portsmouth claims to have their support.
Anthony De Larrinaga, a media analyst at WestLB Panmure, described Johnston as "like a dog to Portsmouth's lamp-post. It is marking out its territory."