WASHINGTON — President Trump has invited Prime Minister Najib Razak of Malaysia to visit the White House in September despite Mr. Najib’s involvement in a billion-dollar corruption scandal.

The White House said in a statement on Wednesday that the visit was intended to “strengthen and broaden our bilateral relationship and expand regional cooperation with one of America’s closest partners in Southeast Asia.”

The invitation represents a significant boost to Mr. Najib’s international standing and is likely to put to rest rumors in Malaysia that he would be arrested the next time he stepped on American soil. In July, the Justice Department filed a civil complaint in a money-laundering case outlining how Mr. Najib, identified as “Malaysian Official 1,” received $731 million from a government fund he oversaw. Investigators around the world are tracking the money trail to his bank accounts in what has become a billion-dollar scandal.

Critics say the visit, scheduled for Sept. 12, also demonstrates that the Trump administration places concerns about corruption well behind other issues. Mr. Najib is yet another visitor to the Trump White House with a history of suppressing free speech and intimidating the political opposition, said Robert G. Berschinski of the advocacy group Human Rights First.