"There are those who are trying to spin what is a debate about the future and security of our country as a personal attack that never happened," Naftali Bennett said at an education conference at the Dead Sea.
"If the prime minister was hurt, I'm very sorry," Bennett said.
Media reported that Netanyahu had threatened today to sack Bennett from the cabinet if he refused to apologise for his criticism in the past few days.
Bennett leads the far-right Jewish Home party, which has close ties with the Jewish settler movement. It has 12 seats in parliament and is a member of Netanyahu's coalition.