Dato' Sri Haji Mohammad Najib bin Tun Haji Abdul Razak is the sixth and current Prime Minister of Malaysia.
Earlier, in an opinion piece published by political website The Hill, Mr Najib assured the United States that Malaysia was a firm partner in its foreign policy objectives, especially in the fight against ISIS.
Mr. Trump didn't mention the investigation during his public appearance with Mr. Najib.
President Trump lavished praise Tuesday on scandal-scarred Malaysian Prime Minister Najib Razak, who has set up camp at the Trump International Hotel, according to a report.
But it has been at the center of investigations in the United States and several countries amid allegations of a global embezzlement and money-laundering scheme.
White House press secretary Sarah Sanders said this week that the Justice Department investigations were not expected to arise when Trump meets Razak in the Oval Office. He said: "We bring to the table a great deal of value propositions". The White House said it would not comment on the US Department of Justice investigation.
Malaysian trade officials said the visit would be an opportunity for Malaysia to explain the trade data discrepancy recorded, and that Malaysia's contribution to the United States trade deficit in goods in 2016 was only 3.37 percent.More news: Amazon on hunt for location to build a second North American headquarters
"No prime minister of Malaysia in the past 60 years had to face such phalanx of worldwide media hostility or avalanche of adverse press publicity both in the United States and the world", he said in a statement.
Flanked by top advisers in the Cabinet Room, Najib told Trump that Malaysia Airlines would buy 25 Boeing 737 jets and eight 787 Dreamliners, and would probably add another 25 737s in the near future - a deal he said would be worth more than $10 billion within five years.
There are about 28,000 Malaysians living in cities throughout the United States.
Mr Najib said Malaysia's successful counter-terrorism offensive was possible through promoting moderation and through a deradicalisation program that has had a 90 per cent success rate.
"Not only is Mr Najib known for imprisoning peaceful opponents, silencing critical media and reversing Malaysia's progress toward democracy", the paper wrote.
A senior USA official acknowledged it was unusual to meet with Najib while 1MDB was under regulatory scrutiny.
The U.S. Justice Department in June moved to seize more than a half a billion dollars in assets related to the 1MDB case, including a Picasso given to actor Leonardo DiCaprio, the screen rights to two Hollywood movies and a $27 million diamond necklace belong to Najib's wife, Rosmah Mansor.