The two leaders played golf together a few years ago at Mr. Trump’s golf club in Bedminster, New Jersey. Mr. Trump signed a photo of the two of them together, “To my favorite prime minister.”
When they meet at the White House, they are expected to discuss the nuclear threat posed by North Korea’s ruler, Kim Jong-un, as well as China’s growing influence in Southeast Asia. Mr. Trump sorely needs an Asian ally who can help on both fronts.
For Mr. Najib, a White House handshake will show voters back home that he can set foot on American soil without being jailed, analysts and opposition members said.
“He can say, ‘I am not wanted in the United States and I can go there without being arrested,’” said Tony Pua, a member of Parliament and a critic of Mr. Najib.
Simply avoiding arrest on a United States visit might seem a low bar for a world leader.
But in Malaysia, the Justice Department investigation has undermined Mr. Najib’s assertions that nearly $681 million deposited in his personal bank accounts was a gift from an unnamed Saudi donor.
The Justice Department said last year that the source of $731 million in Mr. Najib’s accounts was actually the Malaysian government fund.
Mr. Najib has said that he committed no wrongdoing. His office declined to comment for this article.
“From a pure public relations point of view, it’s a meeting the White House should avoid,” said Donald Greenlees, an authority on Southeast Asia with Australian National University. “Even a photo op with Kim Jong-un would be better.”
Among those highlighted in the assets seizure cases are Mr. Najib, who is identified in court documents as “Malaysian Official 1”; his wife, Rosmah Mansor, who is renowned for her foreign shopping excursions; and his stepson, Riza Aziz, whose company, Red Granite Pictures, produced “The Wolf of Wall Street” and other films.
In the United States, Ms. Mansor may find it best not to wear jewelry that the Justice Department wants to seize, including her $27.3 million necklace with a 22-carat, pink diamond pendant, or the 27 gold necklaces and bracelets that she acquired in Los Angeles for $1.3 million.
Also caught up in the scandal are the actor Leonardo DiCaprio, who received more than $12 million in art work, and the model Miranda Kerr, who received more than $8 million in diamond jewelry. They received the items as gifts from Jho Low, a friend of Mr. Aziz who played a key role in establishing the Malaysian fund.
The department says the money used to acquire the property and luxury goods was diverted from One Malaysia Development Berhad, the investment fund that Mr. Najib headed.
Last month, the Justice Department filed a motion to stay the forfeiture cases so that they would not have “an adverse effect on the government’s ability to conduct the related criminal investigation.” A hearing is scheduled for Sept. 18 in Los Angeles.
While Mr. Najib might wish for Mr. Trump to halt the Justice Department investigation, that would seem unlikely given the department’s independence. After all, Mr. Trump has been unable to stop an investigation into Russian election meddling that is headed by Robert S. Mueller III.
“This is a meeting of two leaders who both have legal problems, so it is bound to raise eyebrows,” said Wan Saiful Wan Jan, chief executive of the Institute for Democracy and Economic Affairs in Kuala Lumpur. “If they have a one-on-one meeting, no one really knows what transpires in that session.”
Mr. Najib is the latest in a growing line of world leaders to receive invitations from Mr. Trump, including President Abel Fattah el-Sisi of Egypt and President Rodrigo Duterte of the Philippines, who exert harsh authoritarian control over their countries.
Both the Malaysian leader and Mr. Trump have removed top officials from their roles, but Mr. Najib has also taken much more aggressive steps to protect his hold on power.
In 2015, Mr. Najib fired Malaysia’s attorney general to stop an investigation into the theft of government funds, and named a new one who quickly cleared Mr. Najib of any wrongdoing.
The opposition leader, Anwar Ibrahim, is serving a five-year sentence for sodomy in what critics and rights advocates say is a politically motivated case.
When members of his own party criticized Mr. Najib, he removed them from their posts.
His government has blocked unfriendly news outlets and charged a political cartoonist, Zulkiflee Anwar Ulhaque, with nine counts of sedition. Mr. Zulkiflee, known as Zunar, often depicts Mr. Najib as the “Man of Steal” and his wife, Rosmah, with a giant diamond ring. He faces up to 43 years in prison.
Mr. Pua, the member of Parliament, was sued by Mr. Najib for defamation and is now under a court injunction limiting what he can say about the prime minister.
Mahathir Mohamad, 92, who served for 22 years as prime minister and is now a leader of the opposition, said Malaysia has turned into a “dictatorship” under Mr. Najib where the rule of law is no longer enforced.
Mr. Najib controls the media and nearly every aspect of government, he said, and critics are arrested and detained without due process.
But Mr. Najib’s visit to the White House will not give him the legitimacy he seeks because of Mr. Trump’s own standing, said Mr. Mahathir, who was seen as authoritarian when he was in power..
“I would be very worried if he was making a visit to a very highly respected president of the United States,” he said. “But Trump is not a highly respected president, even in the United States. He himself is under investigation and he has been very erratic.”
Mr. Mahathir added: “Whether he supports Najib or not, he is not going to make much of an impact. If he says Najib is a great leader, people will say, ‘Well, that’s Trump. We don’t take him seriously.’”