Further criticism came from Davey on X, who posted: "Kemi Badenoch has once again shown unbelievably poor judgement by failing to back two British MPs denied entry to Israel.
"Yet another complete shocker."
Foreign Affairs Committee chairwoman Dame Emily Thornberry told Sky News she was "completely gobsmacked" by Badenoch's comments.
"This is nonsense," the Labour MP said. "You have to stand up for what's right, Kemi Badenoch, and you should stand in solidarity with other parliamentarians who were just going to Israel and the West Bank to find out what was going on."
Badenoch was also contradicted by Tory MP Fuller, who told LBC that Conservative MPs had experienced similar issues in China and he wanted to support the right to travel to other countries.
"I want to support my colleagues," said Fuller. "This isn't a partisan thing, as a parliamentarian, we live in a difficult world at the moment.
"Democracies are under threat, we should support them in those circumstances, whether China, Israel, or anywhere...
"On this, my personal view is, parliamentarians should be allowed free passage to other countries, to our allies. We should look at that in a poor light. We should be supporting them."
Fuller spoke about his boss again on Times Radio, saying he thought MPs on official trips are "going there to be better informed about the situation and then report back to their parliamentary colleagues about what they have found".
"Democracy isn't a guarantee in life," he said. "Freedom isn't guaranteed."