The fund, set up by Najib in 2009 with the stated aim of boosting the Malaysian economy, had defrauded Malaysians "on an enormous scale", BBC quoted US Attorney General Loretta Lynch as saying.
Najib, identifiable as "Malaysian Official 1" and whose account allegedly received millions in funds originating from 1MDB, has consistently denied any wrongdoing.
US authorities on Wednesday said it were moving to seize more than $1 billion assets related to the fund which would make up only a proportion of the more than $3.5 billion allegedly diverted.
Najib was officially cleared of criminality by the Malaysian attorney general earlier this year. The attorney general was dismissed after he repeatedly criticised the prime minister's handling of the case.
The current attorney general, Mohamed Apandi, said on Thursday that there was no evidence funds were misappropriated from 1MDB.
Former premier Mahathir Mohamad said there "can be no doubt" that Najib was responsible for 1MDB's finances.
He said Malaysians should stage street protests against Najib, as they have in the past, and push for a referendum on his leadership.
Parliamentary opposition leader Wan Azizah Wan Ismail said he should go on leave "so as not to create the perception of abuse of power" or hinder this "very important" investigation".
A spokesperson for Najib said the government would "fully co-operate with any lawful investigation in accordance with international protocols".
"As Najib has always maintained, if any wrongdoing is proven, the law will be enforced without exception."
1MDB said in a statement last year that it had never given money to the prime minister and called the claims "unsubstantiated".
Meanwhile, Singapore fraud investigators said on Thursday they had seized more than $175 millions in assets connected to 1MDB and found several major banks, including Standard Chartered, had showed "weaknesses in the processes for accepting clients and monitoring transactions".
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