Global Radio has been given five weeks by the Takeover Panel to make a formal offer for GCap Media or walk away.
The panel said Global Radio, the privately owned group chaired by former ITV boss Charles Allen, must indicate a firm intention to bid for GCap by 5 March or refrain from bidding for six months.
GCap, the owner of Classic FM and Capital 95.8, rejected a £313m bid by Global, last month, saying the offer of 190p a share in cash "significantly undervalued the company". Its chief executive Fru Hazlitt branded the offer "derisory".
GCap welcomed the "Put up or Shut up Deadline" imposed by the regulator.
"By 5 March, Global Radio will have had more than 11 weeks since its initial approach and more than three weeks since Fru Hazlitt's presentation of her plans for the group to make a decision," a statement from the company said.
GCap, which was formed after Capital Radio bought GWR Group Plc in 2005, had a value of £700m at the time of the merger but its market capitalisation had fallen to around £200 before speculation of the bid emerged.
Global, which runs the Heart, Galaxy and LBC networks, is keen to build up its business after losing out to German company H Bauer in the battle for Emap's radio assets.
Analysts expect Global to come back with a higher offer. "We expect Global to raise its offer to circa 210p and thereby secure board recommendation," Numis said in a research note.
GCap reported higher third-quarter revenues yesterday, despite a drop in listeners, and said it had seen no evidence so far of a downturn in radio advertising.
The group said like-for-like revenues rose four per cent in the three months to 31 December and that revenues for January were expected to climb 7 per cent.
"Current trading is in line with our expectations and the radio advertising market remains stable, with no evidence to date of any downturn," the company said.
However, data from the Radio Joint Audience Research revealed that total year-on-year listening figures at the group's radio stations fell to 14.8 million in the quarter from 15 million.
The data also showed no improvement in market share for GCap's flagship station, 95.8 Capital, once the favourite station in London but now in third place behind Heart and Bauer's Magic 105.4.