Corbyn was forced to cancel a campaign trip to Wales but denied there was a crisis after senior party member and former London mayor Ken Livingstone was suspended for linking Adolf Hitler to Zionism.
Labour deputy leader Tom Watson told BBC radio that the remarks about Hitler were "provocative" and "obviously caused great offence", promising "zero-tolerance" against anti-Semitism.
"We are going to deal with this," he said.
The dispute has been simmering for months -- ever since veteran socialist Corbyn was elected party leader in September.
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In February, Labour launched an investigation into its Oxford University student branch after the chairman stepped down complaining that many members "have some kind of problem with Jews".
Last month Vicki Byrne, deputy chairwoman of a local party branch, was suspended after it was reported she had posted anti-Semitic remarks on Twitter.
Corbyn's own brother was drawn into the row earlier this month when he dismissed complaints about anti-Semitic abuse as part of an argument about Israel.
Defending Shah in a series of interviews on Thursday, Livingstone also said that criticism of Israel's policies was being confused with anti-Semitism.
"When Hitler won his election in 1932 his policy then was that Jews should be moved to Israel. He was supporting Zionism before he went mad and ended up killing six million Jews," he said.
"I have been in the Labour Party for 40 years and I have never heard anyone say anything anti-Semitic.