That fight would most likely end up before the Supreme Court, the two said, with Trump's attorneys having to defend why the returns should remain private. It seeks an injunction to stop what the two alleged are the president's constitutional violations.
Mr Frosh and Mr Racine cited Mr Trump's leases, properties and other business "entanglements" around the world as the reason for the suit, saying those posed a conflict of interest under a clause of the constitution.
The suit says that Maryland and D.C. are now being forced to either give the Trump Organization special treatment or refuse and watch other states that do give it special treatment profit.
Another example alleging wrongdoing that Racine and Frosh pointed to is the continued use of the president's hotels by foreign governments.
In January, trump said that his business assets will be managed by his sons, in order to avoid possible conflict of interest.
A White House spokesman did not immediately respond to a request for comment Monday.
The Republican National Committee called the lawsuit "absurd".
"The actions by the attorneys general represent the kind of partisan grandstanding voters across the country have come to despise", the RNC said in a statement to the New York Times.
While a number of legal challenges have been filed accusing Trump of corruption, the latest suit is the first brought by government entities.
Ahead of the Monday lawsuit, the U.S. Department of Justice filed a 70-page legal brief on Friday arguing that Trump's businesses are legally permitted to accept market-rate payments from foreign governments while he is in office.
The President and his attorneys argue the clause does not cover fair-value transactions, such as hotel room payments and real estate sales.
Trump has refused to release his tax returns to date, breaking with decades of precedent set by previous US presidential nominees.
A suit filed by a nonprofit watchdog group in January, and another filed by a group of restaurants in March, have both run into trouble over the question of standing ― that is, the question of whether the plaintiff has actually been harmed by what the defendant is doing.
The attorney generals of Maryland and Columbia plan to file a lawsuit that foreign payments to President Trump violate the U.S. Constitution, according to reports. A signed copy of the lawsuit reportedly alleges "unprecedented constitutional violations" by Trump.
Frosh outlined details of the lawsuit in an interview with The Associated Press. And government further said that Trump's hotel revenues do not fit the definition of an improper payment under the constitution.
But Racine and Frosh told the Post on Sunday that Trump had broken promises to separate himself from his business interests, the Post said, noting that the president receives regular updates on his company's finances. Trump's refusal to release his tax returns, which would reveal more about his enterprises, could become part of the case.