After being pictured with Mr Bush, the TV host said she was friends with many people who don’t share her views, adding we should “be kind to everyone”.
But Hulk actor Ruffalo said Mr Bush should be “brought to justice for the crimes of the Iraq War”.
He added “we can’t even begin to talk about kindness” until that happens.
However the likes of Reese Witherspoon, Jamie Foxx and Jennifer Garner backed DeGeneres.
The TV host and comic sparked a fierce debate on social media after sitting next to Mr Bush, who was in power from 2001 to 2009, at an NFL match at the weekend.
“People were upset,” DeGeneres said on her show. “They thought, why is a gay Hollywood liberal sitting next to a conservative Republican president?”
The former president has faced condemnation for leading the country into war with Iraq and Afghanistan, and he also opposed gay marriage while in office.
The talk show host explained that she was indeed friends with Bush, adding: “When I say, ‘Be kind to one another,’ I don’t only mean the people that think the same way that you do. I mean
be kind to everyone. Doesn’t matter.”
On Instagram, Witherspoon replied with the word “Exactly” accompanied by a bullseye emoji. Foxx said: “Thank uuu very much for that!!!! Soooo needed and Necessary.” Garner chimed in with: “Ellen! You are amazing! ♥️”
Singer Lenny Kravitz offered: “Let Love Rule!”, Kendall Jenner contributed a flurry of exclamation marks and love heart emojis, and actress Kristen Bell added her voice.
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Bell’s The Good Place co-star Jameela Jamil also praised the talk show host for her “incredibly strong” handling of the controversy.
But the British actress then rowed back after being bombarded by comments from critics of the former president.