The band had come under an enormous amount of criticism over the show and had received pleas from campaigners and several of their peers to cancel, as part of a widespread cultural boycott in the country.
They said that the band would be displaying double standards by performing in a country where "a system of aparthied is opposed on the Palestinian people".
Rather than agree to a meeting, however, Yorke responded with an open letter of his own 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," he wrote, "some more liberal than others. As we have in America. We don't endorse Netanyahu any more than Trump, but we still play in America."
Ex-Pink Floyd member Roger Waters accused Yorke of "whining" and slammed him for his lack of communication with critics.
"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 to managed to affect by chatting with musicians," he said.
Enjoy unlimited access to 70 million ad-free songs and podcasts with Amazon Music Sign up now for a 30-day free trialSign up
According to Richard Ferrer, editor of the London-based Jewish News, there was a "melting pot" of fans in attendance.
He tweeted a photo of the band onstage and quoted Yorke telling the crowd: "A lot was said about this, but in the end we played some music."
According to reports, Radiohead performed a 27-song set and two encores, including some of their rarely-played tracks "Creep", "Karma Police" and "No Surprises".
The BBC also reports that the show was the band's longest set since 2006, with 27 songs in a performance that included two encores.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies