WASHINGTON—Special Counsel Robert Mueller was authorized in a secret memo to investigate former Trump campaign chairman Paul Manafort’s work for the Ukrainian government, in addition to alleged collusion with Russian officials to interfere in the 2016 elections, according to court filings.

The classified August memo from Deputy Attorney General Rod Rosenstein was disclosed in a court filing by Mr. Mueller’s prosecutors. It seeks to counter arguments by Mr. Manafort’s lawyers that his indictment should be thrown out. Mr. Manafort has denied the allegations and pleaded not guilty to indictments filed by Mr. Mueller’s team in federal courts in Alexandria, Va., and Washington.

Lawyers for Mr. Manafort, who served for several months in 2016 as Mr. Trump’s campaign chairman, argued in court filings that the deputy attorney general had only authorized Mr. Mueller to investigate matters strictly arising from the main subject of the investigation: Russian interference in the election and links between the Kremlin and Mr. Trump’s campaign.

They said that the indictments lodged against Mr. Manafort were faulty because they dealt with charges unrelated to the Kremlin’s meddling.

Mr. Manafort has denied any wrong doing and pleaded not guilty to the indictment lodged against him Washington. He was charged with conspiring against the U.S., conspiring to commit money laundering, acting as an unregistered foreign agent and false-statements. He has also pleaded not guilty to a subsequent indictment in federal court in Alexandria, Va., that alleges he committed tax and bank fraud.

Between the two cases, he is accused of laundering $30 million through offshore accounts and using false statements to obtain $25 million in bank loans. He is set to first stand trial in Alexandria in July. A trial on the charges in Washington is slated for September.

The Russian government has denied it meddled in the 2016 election, and Mr. Trump has called Mr. Mueller’s investigation a “witch hunt.”

Mr. Mueller’s prosecutors wrote in court papers filed late Monday that they were, in fact, authorized by Mr. Rosenstein to investigate and try Mr. Manafort on the Ukrainian-related charges.

Citing Mr. Rosenstein’s initial memo appointing Mr. Mueller in May, they noted they had a broad mandate. They wrote that the memo was worded in a way that clearly was meant to include allegations related to Mr. Manafort’s work for Ukraine.

The longtime political consultant worked for Ukraine’s former president, Victor Yanukovych, who was described by the special counsel as being “a Russia-backed Ukrainian politician.” He also had a business relationship with a powerful Russian oligarch, Mr. Mueller’s prosecutors wrote.

“An investigation of possible ‘links and/or coordination’ between the Russian government in its political-interference campaign and ‘individuals associated with the campaign of President Donald Trump ’ would naturally cover ties that a former Trump campaign manager had to Russian associated political operatives, Russian-backed politicians, and Russian oligarchs,” the prosecutors wrote, citing language in Mr. Rosenstein’s original memo.

In August, Mr. Rosenstein further clarified Mr. Mueller’s mandate in a classified memo that the special counsel attached in redacted form to its filings.

In that memo, Mr. Rosenstein authorized Mr. Mueller to investigate whether Mr. Manafort committed potential crimes “by colluding with Russian government officials with respect to the Russian government’s efforts to interfere with the 2016 election for President of the United States, in violation of United States law.”

It further stipulated that Mr. Mueller was permitted to probe Mr. Manafort for any crimes “arising out of payments he received from the Ukrainian government before and during the tenure of President Viktor Yanukovych. ”