Conway, one of the White House figures who is most prominent in the media, allegedly broke that law multiple times.
"As a highly visible member of the administration, Ms. Conway's violations, if left unpunished, send a message to all federal employees that they need not abide by the Hatch Act's restrictions," Henry J. Kerner, appointed by Trump to head the OSC in 2017, said in a letter to the President.
"Her actions erode the principal foundation of our democratic system - the rule of law."
The OSC said in the letter that Conway "violated the Hatch Act on numerous occasions by disparaging Democratic presidential candidates while speaking in her official capacity during television interviews and on social media".
The agency determined last year that Conway had violated the 1939 law by promoting the Senate candidacy of Roy Moore, a former Republican Judge accused of sexually abusing minors and who ultimately lost his bid for a seat in the Upper House.
In 2017, in addition, Conway, had to get legal advice after pushing on television the clothing line of Ivanka Trump, the President's oldest child and a business magnate in her own right.
Other instances cited in the OSC report include Conway's remarks on Fox News disparaging Democratic candidates such as former Vice President Joe Biden, Senators Bernie Sanders, Elizabeth Warren, Cory Booker and Amy Klobuchar and former Congressman Beto O'Rourke.
Trump did not comment on the matter during a White House event with governors on Thursday, which Conway attended, and his office said that he was not planning to take any action against his influential adviser.
White House spokesman Steven Groves told Efe news that "the unprecedented actions of the OSC against Conway violate her constitutional rights to freedom of expression and due process".
White House counsel Pat Cipollone wrote in a lengthy rebuttal letter to the 17-page OSC report that it "is based on multiple fundamental legal and factual errors, makes unfair and unsupported claims against a close adviser to the President, is the product of a blatantly unfair process that ignored statutory notice requirements, and has been influenced by various inappropriate considerations".
"OSC's overbroad and unsupported interpretation of the Hatch Act risks violating Conway's First Amendment rights and chills the free speech of all government employees," he added.
Conway was Trump's third and last campaign chief during his 2016 presidential campaign, and since he entered office she has been closely involved in issues related to party policy and election strategy.