Biggleswade Town Council has said the cull is no longer "an immediate priority".
The town council proposed to remove the birds sensitively using bait containers, and then they would be humanely shot.
But news of the process prompted outrage locally, with the scheme branded "inhumane" and "unnecessary".
An online petition attracted more than 1,200 signatures as many residents disagreed with the idea.
The council's town centre management committee was informed there were difficulties persuading office owners with suitable roofs to agree to allow the bait traps to be laid.
It was intended to start proceedings before the pigeons' peak breeding season last month. But no progress has been made so far, a town council meeting was told on Tuesday. (April 12)
Local resident Leanne Thurlow requested an update on the time frame for the proposed pigeon cull in the town centre.
"Has the town council been able to engage with the numerous organisations which have offered their advice and assistance, and most notably the humane wildlife solutions?" she asked, during the meeting's public open session.
Town mayor Madeline Russell replied: "The update is it's not been a priority at the moment. We'll be looking into things in the future.
"We haven't contacted the particular organisation you emailed us about. But we'll be considering what we can do with this situation.
"It's not the immediate priority on the agenda of the town council."
Councillor Mark Knight explained the extent of the problem, telling the council's town centre management committee in February: "I did take a few photos of the pigeons the other day just after they'd landed on one of the roofs and taken off.
"There are too many to count unless you get them in a picture," he explained. "I counted more than 50 pigeons, and I think there are at least two flocks.
"So there's been considerable growth in the size of the flocks during the year we've been reviewing this. There's some urgency, and it's certainly true pigeons breed all year."
He also said at that meeting: "My understanding is the proposal is to capture them in a humane way and then shoot them."