The BBC said Martin and Coldplay drummer Will Champion were in the studio to discuss the band's latest CD, "Viva La Vida or Death And All His Friends."
Martin quickly exited the studio, however, after stating he was "not really enjoying this" and didn't like "having to talk about things."
The singer's departure came soon after host John Wilson asked him about remarks he made at a 2005 music awards ceremony in which he said his band would be away "for a very long time," the BBC said.
"I always say stupid things and I think Radio 4 is the place that will most remind me of that," he said.
Asked if the new CD's title reflected a lyrical obsession with death on the part of the band, Martin replied: "I wouldn't agree with you there at all, no. I'd say you're journalistically twisting me into saying something I don't really mean."
After the singer left, Wilson interviewed Champion until Martin returned to answer one final question, the BBC said.
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards
Biologists detail four new deep-sea 'killer sponges'