The Coral Gables-based subsidiary of Odebrecht, the Brazilian engineering and construction conglomerate, sued the state Monday over a contentious new Florida law that bans governments from hiring companies with business ties to Cuba.

The lawsuit, filed in Miami federal court, contends that the law is unenforceable and unconstitutional because it sets foreign policy — a power that the courts have ruled belongs solely to the federal government.

The law would prohibit state and local government agencies from awarding contracts worth at least $1 million to Odebrecht Construction Inc. — among others — because a subsidiary of its parent company is upgrading the Cuban Port of Mariel.

Gov. Rick Scott caused an uproar last month when he signed the law in a ceremony at Miami’s Freedom Tower, only to issue a statement shortly afterward suggesting the law was unconstitutional. The governor later retreated from that stance, saying he backed the law and that his administration would defend it against a likely legal challenge.

A Scott spokesman declined to comment Monday because the governor’s office had not yet received a copy of the lawsuit.

Sen. Rene Garcia of Hialeah, one of two Miami-Dade Republicans to sponsor the legislation, which received near-unanimous support from state lawmakers, said the court should uphold the law.

“This is not about foreign policy,” he said after learning about the lawsuit from a Miami Herald reporter. “I see it as a states’ rights issue. We have a right to decide who we want to do business with.”

In its lawsuit, however, Odebrecht argues that federal laws “do not authorize states to enforce their own sanctions against Cuba.”

The company also notes that it complies with the U.S. embargo on Cuba and “is remote and distant from, and has no contact with,” COI Overseas Ltd., the company working on the Port of Mariel for Brazil-based parent company Odebrecht S.A. Neither the Cuban affiliate nor the parent company work in Florida, the lawsuit says.

Florida-based “Odebrecht USA does not engage, and never has engaged, in business operations in Cuba,” the company said in a statement Monday in which it lamented having to sue a state agency “with which we have worked so successfully in the past.”

Odebrecht sued Ananth Prasad, secretary of the Florida Department of Transportation. Though FDOT has not denied Odebrecht the ability to compete on any bids yet, the agency informed the company that it plans to enforce the new state law when it is scheduled to take effect July 1. Odebrecht intends to bid on approximately $3.3 billion in FDOT contracts this year, the lawsuit says.

Odebrecht is seeking a temporary injunction to forbid immediate enforcement of the law, said the company’s lawyer, Raoul Cantero, a former Florida Supreme Court justice who is now a partner with the Miami law firm White & Case.

“We think the statute is illegal on its face, regardless of anybody bidding on anything,” Cantero said.

As precedent, Cantero cited a 2000 U.S. Supreme Court ruling striking down a Massachusetts law restricting business with companies tied to Myanmar. He also referred to two local cases.

In 2000, a federal judge ruled against Miami-Dade County’s requirement that companies submit sworn statements saying they did not work in Cuba. In 2009, another federal judge overturned a 2008 Florida law requiring travel agencies specializing in trips to Cuba to pay increased fees and bonds.