Thomas, who will be celebrating her 90th birthday soon, made the remarks in a talk with Rabbi David Nesenoff on the margins of an event held by President Obama last week to mark Jewish heritage month.
After being asked for her opinion of Israel, Thomas responded by saying: "Tell them to get the hell out of Palestine."
Turning her attention to the Palestinians, she said, "Remember, these people are occupied. And it's their land," adding the Jews should "go home" to Poland and Germany.
Thomas' remarks have prompted numerous calls for her resignation. One of those who spoke out against her is Ari Fleischer, the former White House spokesman during President George W. Bush's presidency.
"She should lose her job over this," Fleischer told the Politico website. "As someone who is Jewish, and as someone who worked with her and used to like her, I find this appalling."
As a daughter of Lebanese immigrants, Thomas has not been hiding her sympathy for the Arabs and Palestinians in questions she asked at White House press briefings. She has referred to the lethal raid on the Gaza-bound Marmara ship Monday as a "massacre."