Ms Thomas, who has been a presidential correspondent since the Kennedy administration, has now been dropped by the speaking agency she worked for.
A speech at a high school graduation event was also cancelled by the principal in the wake of the remarks.
Ari Fleischer, a former George W Bush Press Secretary, said her comments advocated “religious cleansing” and that she should be fired.
He said: "As someone who is Jewish, and as someone who worked with her and used to like her, I find this appalling."
How can Hearst stand by her? If a journalist, or a columnist, said the same thing about blacks or Hispanics, they would already have lost their jobs."
Another former Bill Clinton adviser said she had showed herself to be an antisemitic bigot.
Lanny Davis said: “Her statement is an ancient and well-known antisemitic stereotype of the alien Jew not belonging in the land of Israel that began 2,600 years with the first tragic and violent Diaspora caused by the Romans.”
In a statement Ms Thomas said she regretted her comments.
She said: “They do not reflect my heartfelt belief that peace will come to the Middle East only when all parties recognise the need for mutual respect and tolerance."
But Abraham Foxman, national director of the Anti-Defamation League, said her apology did not go far enough.
He said: "Her suggestion that Israelis should go back to Poland and Germany is bigoted and shows a profound ignorance of history.
"We believe Thomas needs to make a more forceful and sincere apology for the pain her remarks have caused."
President Obama has not made any comment about the controversy.
