David Beckham's plan to bring a Major League Soccer franchise to Miami looks to be on life support after the city's mayor, Tomás Regalado, previously a key ally in the project, said no to the construction of a stadium at a prime waterfront site.

The surprise rejection was the second time in a month that the former England captain had been rebuffed in his efforts to build a 25,000-seat stadium to launch his team at a favoured city-centre location, after the collapse of his similar proposal at the Port of Miami.

Beckham's investment group, which includes the entertainment impresario Simon Fuller and the Bolivian telecoms billionaire Marcelo Claure, said it would pause to consider its options, one of which will presumably be withdrawing from the project altogether.

"We presented a strong proposal for the site suggested to us by the two mayors [Regalado and the Miami-Dade county mayor, Carlos Giménez]," the group, Miami Beckham United, said in a statement after a meeting on Tuesday with city officials in Miami.

"Our package was the most equitable soccer stadium proposal that Miami, or any other city in America, has ever seen, 100% privately funded without any local taxpayers' money.

"Our team will now pause and weigh alternatives. The people of Miami deserve a team and stadium that they will be proud of for decades to come."

The statement added that the group had experienced "an incredible level of support and passion from every community in Miami" in its efforts to launch a team in the city.

Beckham, who was canvassing support in Miami last week while the England team was in town for its final two World Cup warmup games, had believed he had Regalado's support for the stadium, which would have been built adjacent to the Miami Heat basketball team's American Airlines Arena on Biscayne Boulevard.

The project, which would have involved filling in a disused deep-water slipway and the creation of what Gimenez described as a "grand waterfront park", was suggested to Beckham's group in May. It quickly became their favoured plan B once it was clear that opposition to the port plan from the Royal Caribbean cruise line and a maritime workers' alliance would prove difficult to overcome.

At the time, John Alschuler, Beckham's New York-based real estate adviser, told the Guardian that he welcomed the proposal from Giménez as "a meaningful step forward". He said: "Instead of having one good option, we now have two."

The rejection of the slipway site by Regalado, coupled with the opposition to the Port of Miami plan, effectively leaves Beckham with none, at least on the waterfront. While maintaining the diplomatic public position of being open to all alternatives, he is known not to favour other possible inland sites, such as next to the Miami Marlins' new baseball stadium in Little Havana.

At a press conference in Miami in February, at which Beckham announced he was taking up his option to launch his own MLS franchise in the city, he spoke passionately of creating a club with a community feel, where fans could walk together along picturesque waterfront boulevards to a state-of-the-art stadium with all the benefits of a central location.

Regalado said he had changed his mind about the waterfront site and considered it inappropriate for a football stadium after seeking the opinions of local residents. He said he had conveyed those objections to Beckham's representatives.

"They were disappointed but at the same time they didn't want to fight the residents and I think that's a good thing," Regalado said.

"They want to be welcomed, they want to be here as good neighbours. We had a good meeting because they know we represent the residents and they want to have good terms with the residents."

Regalado said he had "deep respect" for Beckham and his partners and expressed a desire to help the group find an alternative site.

Giménez said he also wanted Beckham's focus to remain in Miami. "If asked by Major League Soccer and Miami Beckham United, my administration will work to identify other possible sites in Miami-Dade county," he said in a statement.

"I am a big supporter of bringing Major League Soccer to Miami-Dade because I know it would be successful here. However, my terms will not change: no taxpayer dollars will go towards the construction of a stadium."