The friction between the two centres on the outcome of Ofcom's radio industry review due out in a few weeks.
Earlier this summer, Ofcom chief executive Stephen Carter hinted that two extra national digital multiplexes capable of carrying 20 stations were a possibility.
GCap's executive chairman at the time, Ralph Bernard, responded angrily, claiming that such a move would break the terms on which the first and so far only national multiplex was licensed to Digital One, now owned by GCap and Arqiva (formerly NTL Broadcast).
However, Bernard now seems to be mollified, judging by comments he made at GCap's financial presentation on Wednesday to the effect that GCap now understood it is not Ofcom's intention to make the new services directly competitive with GCap's own.
Bernard is now chief executive of the company, having taken over from the departing David Mansfield.
A GCap spokeswoman was at pains to point out that there had been no discussions with Ofcom about the issue, and Bernard also said there had been no compromise.
Ofcom did not comment, saying only: "We will be in a position to announce our plans for UK radio when we announce the final part of our radio review in October."
Other radio groups greeted GCap's change in stance positively. Emap's managing director of national brands Shaun Gregory called the threat of legal action "almost like a sideshow" and said that GCap had climbed down after realising that the release of additional spectrum was good for the radio market.
Chrysalis Radio chief executive Phil Riley said: "I thoroughly agree with Ralph Bernard that if there were to be a second national multiplex that it needs to be complementary and not competitive. We await Ofcom's radio review with interest."
On Wednesday, GCap said that its analogue stations were to receive extra investment after it found extra money resulting from greater-than-expected cost savings.
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