It sounded like the type of event that Mayor Eric Adams would want to bring to New York City to boost the economy: an elite international golf tournament that would draw visitors and their wallets.

But because the tournament has ties to the government of Saudi Arabia and will be played at a city-owned course run by former President Donald J. Trump’s family business, it has prompted widespread criticism, especially from family members of victims of the Sept. 11 terrorist attacks.

Mr. Adams, whose administration allowed the tournament to move forward, is now facing pressure from the City Council to revisit his stance.

Adrienne Adams, the City Council speaker, and Shekar Krishnan, a member of the Council who leads its Committee on Parks and Recreation, sent a letter on Wednesday night to Mayor Adams and Sue Donoghue, the parks commissioner, urging them to immediately void the city’s contract with the Trump Organization to operate the course at Ferry Point in the Bronx, and to cancel the tournament.

The letter argues that the city has new grounds to end the relationship after the Trump Organization’s longtime chief financial officer, Allen H. Weisselberg, pleaded guilty to felony fraud charges last month. The city’s agreement with the company requires its employees to comply with all federal, state and local laws.

“Public parkland should not be in the hands of Donald Trump or the Trump Organization,” the letter said.

The letter also contends that the “Saudi-backed tournament does harm to the families of 9/11 victims and offends the public memory of that horrific day.”

The City Council, which does not have the authority to revoke the contract, may hold a hearing next week to examine it, Mr. Krishnan said in an interview. He said that he had spoken to victims’ families about their concerns.

“They agree with us about the urgency of the situation,” he said.

Eric Trump, an executive vice president at the Trump Organization, said in a statement on Thursday evening that the company had worked with the city to approve the event.

“We are incredibly proud to host the finest women golfers in the world at Trump Ferry Point,” Mr. Trump said in a statement. “A big thank you to the City of New York and to the Parks Department for their support and approval.”

The organization noted that it would be the second time the tournament would be hosted in New York State. It was held last year at Glen Oaks Club in Nassau County.

The golf tournament, a women’s event that is part of the Aramco Team Series, is scheduled to begin on Oct. 13. The field is expected to include two of women’s golf’s most dependable American stars, the sisters Jessica and Nelly Korda.

Like the LIV Golf series that has upended the highest levels of men’s golf by poaching some top players from the PGA Tour, the Aramco Team Series is linked to the Saudi government’s web of enterprises. Saudi Arabia’s sovereign wealth fund, which is overseen by Crown Prince Mohammed bin Salman, is the “presenting partner” for the series and its title sponsor, Aramco, is Saudi Arabia’s state-owned oil giant.