Conservative MPs Andrew Percy and Sir Eric Pickles had urged Labour to suspend Mr Khan, who was appointed a CBE for his community and interfaith work and is co-founder of The Muslim Jewish Forum of Greater Manchester.
They described his comments as “deeply offensive”.
Joan Ryan MP, chair of Labour Friends of Israel, told the Telegraph: “As the European Forum on Antisemitism has made clear, drawing comparisons between contemporary Israeli policy to that of the Nazis is totally unacceptable.”
Marie van der Zyl, a Board of Deputies vice president, and Sharon Bannister, president of the Manchester Jewish Representative Council, called on Mr Khan, who is MEP for the North-West England region, to apologise.
In a joint statement, they said: "We are deeply disappointed by these tweets, which, whilst not new, are still deeply offensive. We would ask Afzal Khan to withdraw the comment and to publicly apologise for it. There is no place for antisemitism in our politics."