The claims have been made by Telford and Wrekin Green Party's coordinator Pat McCarthy, who stood for the Wrekin constituency in the General Election, after Labour candidate for Telford , Kuldip Sahota rejected the offer over the seat he was contesting.
Mr Sahota lost by just 720 votes to the Tories' Lucy Allan, while the Green Party's Luke Shirley received 898 votes, which Mr McCarthy said could have gone to the Labour Party in Telford under the agreement.
However, Mr Sahota said it might have helped him win the seat, but that the party nationally did not want to pursue it.
Mr McCarthy said: "We would like to scotch a few myths about why, given that the Labour Party had adopted many of our 2015 policies, we didn't step down in marginal Telford to allow Kuldip Sahota to take the seat.
"We believe that progressive alliances, a mutually beneficial agreement between two parties that share similar values is the next best thing to proportional representation as it allows voters more say with their vote.
"We offered Telford Labour Party the possibility that we would stand down in this general election.
"We wanted to negotiate a mutually advantageous deal for the local elections in 2019 and our view was that Labour would come out of it with an additional seat.
"It was openly discussed at Telford and Wrekin Green Party meetings and we would have supported Labour canvassers on the door step to get our message across that this was the best way to keep the Conservatives out of Telford and forge a cooperative role for the Greens in local politics.
"Yes, this is a new co-operative, less divisive way of doing politics but we believe that this would secure a more hopeful future for the Telford electorate.
"The reason we didn't step down is because they rejected the deal we were offering them.
"We offered them a negotiated position and they rejected it before negotiating."
Mr McCarthy also thanked those who had supported the party.
He said: "I would like to thank all the voters in both the Wrekin and Telford constituencies for putting their trust in the Green Party to give both Luke Shirley and myself higher than average support on a day when the smaller parties' vote was squeezed."