Yvonne Davies, the leader of Sandwell Council, is the subject of a probe by Labour Party after a complaint regarding tweets she posted in 2018.
One post features a link to a petition calling for a parliamentary debate over whether Israel has "improper influence" over British politics, while another suggests "Israel's hand" was behind criticism of Jeremy Corbyn.
John Spellar, the Labour MP for Warley, today told Councillor Davies to apologise, and also urged the Labour Party to look at how the Labour group in the borough is run.
He said: "It is not for me to prejudge the investigation, but the tweets are clearly cause for concern.
"I would have thought that at the very least she would want to withdraw them and apologise for posting them.
"The Labour Party really needs to look into this – and indeed at how the Labour group in Sandwell is being run at the moment."
Sandwell councillor Paul Moore, who lodged the complaint three months ago, has called for Councillor Davies to step aside as leader until the investigation is concluded.
The Labour councillor for Hateley Heath, said: "The right thing to do would be for Councillor Davies to step aside while these serious allegations are being investigated by the Labour Party."
Birmingham Hodge Hill MP Liam Byrne, Labour's candidate for West Midlands Mayor, has urged his party to urgently deal with the matter.
He said: "As a complaint has been made to the Labour Party, it is right that it is investigated and dealt with quickly and swiftly.
"There is absolutely no place for racism or anti-Semitism in the Labour Party."
It is understood that Labour has received a further complaint about tweets posted by Councillor Davies. One features a link to an article defending former London mayor Ken Livingstone, who at the time was suspended by Labour for alleged anti-Semitism.
Another features a link to an article claiming "the Jewish establishment's 'War Against Corbyn' risks bringing real antisemitism to Britain". It is described by Councillor Davies as "a real breath of fresh air".
Councillor Davies, who represents Langley, became Sandwell Council's third leader in four months when she was elected last May.
She has insisted she is not anti-Semitic and said she would be careful about what she retweeted in future due to there being "a lot of sensitivity" around the issue.
Last night she said she has been told by the Labour Party not to comment until the investigation has been completed.
Since becoming Labour leader Sir Keir Starmer has vowed to prioritise tackling anti-Semitism in the party.