Carmarthenshire council is trying to save £16m over the next three years and said closing Whitland’s recycling centre would save £80,000 annually.
But residents would have to travel about 17 miles (27 km) to reach the nearest recycling centre at Nantycaws, prompting concerns over fly-tipping.
The council said it was “likely to withdraw this proposal” following an “overwhelming” public response.
It said almost three-quarters of the 2,000 people who responded to a budget consultation strongly disagreed with the closure.
It was one of 14 proposals put forward by the council to make savings.
The council said it was still likely to consider changing the opening hours of the centre to save money.
‘Encouraging to hear’
It said its executive board would meet on 24 February to decide on a proposal to take to the full council who will make a final decision.
Speaking to BBC Radio Cymru’s Post Cyntaf programme, Whitland town councillor Ffion Scourfield said: “It’s not a concrete proposal, but it’s encouraging to hear that the centre is likely to stay open.
“There’s been a tremendous response from the community… I’m pleased the county council have taken this seriously.”
Executive board member for resources David Jenkins said: “We continue to face challenges and pressures on our resources, and it’s only right that we look at every area to see how we can better manage the resources we have available…
“We still have a lot of difficult decisions to make over the coming weeks, but I’m sure that those who felt strongly about the Whitland proposal will appreciate knowing how we are inclined to vote at executive board.”