Michael Cohen, a former attorney for President Trump, on Thursday filed a lawsuit against the Trump Organization for not paying legal fees Mr. Cohen alleges he was owed as a result of his work for the company.

In the suit, filed in New York State Supreme Court, Mr. Cohen said he had incurred nearly $2 million in unreimbursed legal fees arising from “multiple” congressional hearings, Special Counsel Robert Mueller’s Russia investigation, and other matters.

He also accused the Trump Organization of having “breached the covenant of good faith and fair dealing,” alleging that the company failed to reimburse his legal expenses “only after it became clear that Mr. Cohen would cooperate in ongoing investigations into his work for the Trump Organization” and into executives at the company.

As of January 2019, Mr. Cohen said his unreimbursed legal fees amount to more than $1.9 million. He said he asked the Trump Organization on Jan. 25 to reimburse him for those fees, but that the company hasn’t responded.

A lawyer for the Trump Organization didn’t immediately respond to a request for comment. Rudy Giuliani, a lawyer for Mr. Trump, on Thursday suggested that Mr. Cohen had started cooperating with investigators because the company stopped paying his legal fees—rather than the reverse, which Mr. Cohen alleged.