LONDON — Lawyers for Elliott Broidy, a Republican fund-raiser close to President Trump, on Monday filed a lawsuit accusing the government of Qatar of hacking into his emails and conspiring with Washington lobbyists to besmirch his reputation.

The lawsuit is one of the first high-profile attempts to hold a foreign government accountable in American courts for cyberespionage. It comes at a time when hacking is becoming an increasingly common tool among a growing number of states seeking to punish enemies or achieve political goals.

“This suit is the first of its kind,” said Lee Wolosky, a lawyer for Mr. Broidy.

Mr. Broidy, a Los Angeles investor, has been an antagonist of Qatar in Washington. He has accused it of supporting Islamist extremism, and he has provided millions of dollars in financial support for think-tank conferences amplifying those criticisms. He has made the same arguments to Mr. Trump and Republican lawmakers.

At the same time, Mr. Broidy also owns a defense contractor, Circinus L.L.C., that in the past year signed a contract worth more than $200 million with the United Arab Emirates and is pursuing another large contract with Saudi Arabia. Both countries are engaged in a bitter dispute with Qatar, the home to a major American military base and vast natural gas deposits.