Associated British Ports (ABP) had told residents living near the Waterfront, Ipswich, that it would carry out the action on Sunday.
It had raised concerns that the birds around its grain stores were a danger to the food supply chain.
But after a petition, which gathered 3,000 signatures, ABP has now suspended the cull.
Ipswich MP Sandy Martin said he would ask the company to look at alternatives.
The online petition, launched four days ago, called on the Labour MP and Prime Minister to intervene in plans for the cull.
Mr Martin said: “Frightening the pigeons away, making sure they can’t get hold of any grain… those are the sorts of things they might be able to do.
“I am going to have a discussion with Associated British Ports and see if they have tried every possible alternative.”
Animal lover Molly Potter, 21, had helped to set up the petition and was also organising a protest during the proposed cull.
“I have a rescue pigeon and seeing how intelligent he is, it completely broke my heart.,” she said.
“We want to find a more peaceful solution.”
In a statement, ABP said it had decided to “suspend the proposed pigeon cull, whilst we take advice from the appropriate environmental organisations on the latest alternative solutions”.
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