Roger Waters has accused Thom Yorke of "whining" over criticism of the band's upcoming gig in Tel Aviv, Israel.
Radiohead are set to play the show on 19 July despite repeated requests for them to cancel by campaigners, as part of an ongoing cultural boycott of the country.
An open letter issued by Artists For Palestine UK - which was signed by artists including Waters, Thurston Moore, Ken Loach and actress Maxine Peake - called on the band to reconsider the gig.
Director Loach also wrote an open letter to Yorke, published in The Independent, which asked the band to "join the cultural boycott of Israel" and urged Yorke to meet with him to discuss it.
Rather than agree to a meeting, however, Yorke responded with a message on Twitter where he argued that "playing in a country isn't the same as endorsing its government".
"We've played in Israel for over 20 years through a succession of governments, some more liberal than others. As we have in America," he continued. "We don't endorse Netanyahu any more than Trump, but we still play in America.
"Music, art and academia is about crossing borders not building them, about open minds and not closed ones, about shared humanity, dialogue and freedom of expression. I hope that makes it clear Ken."
Ex-Pink Floyd member Waters has since hit out at Yorke over his lack of communication regarding the issue.
In a Facebook Live conversation with the Boycott, Divestment and Sanctions Movement, he said: "We should observe the picket line. Anybody who's tempted to do that [gig], like our friends in Radiohead... if only they would actually educate themselves.
"I know Thom Yorke's been whining about how he feels insulted, people are suggesting he doesn't know what's going on. Well Thom, you shouldn't feel insulted because if you did know what's been going on, you would have a conversation with [director] Ken Loach, who's been begging you to have a conversation, or with me, I begged you, Thom."
He added that Yorke's alleged lack of communication was "extremely unhelpful to everybody".
"I look forward to - if you feel like it, when you finish your trip to Israel, because you probably still will go - write me a letter and tell me how much good you did and how much change you managed to affect by chatting with musicians," he said.