The Campaign Against Antisemitism charity (CAA) has written to the Conservative Party over concerns about incidents reported about the Bury group.
Ahead of the local elections last week, Shaf Mahmood, who was selected by the Tories as one of their three candidates for the Redvales ward, had his endorsement from the party revoked in April.
It is understood that Mr Mahmood, published a tweet in 2017 saying "Jews r at it again", which referred to a news item about an Israeli national.
A day earlier, another Bury Conservative candidate, Sham Raja, who was confirmed as a Tory candidate in the Sedgley ward, was dropped by the party after post on his account dating back to 2014 emerged which compared Israeli footballers to "assassins".
At the time, the Jewish Representative Council for Manchester and Region (JRC) said they were "profoundly troubled by the latest revelation of antisemitic social media posts".
CAA has also raised concerns about other incidents to the party.
A CAA spokesman said: "The recent incidents have raised urgent questions about the local association’s vetting processes, how it handles the revocation of endorsements, and whether the association has tolerated or indulged in prejudice towards Jewish people among its membership or has sought to exploit perceptions of such prejudice in any target electorate.
"We have called on the Conservatives to investigate the local association as a matter of urgency.
"Campaign Against Antisemitism advocates for zero tolerance of antisemitism in public life. To that end we monitor all political parties and strive to ensure that any cases of concern are properly addressed."
The Conservative party has been approached for a comment.
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