Rudy Giuliani, personal lawyer to Donald Trump, is facing fresh scrutiny over reports that he tried to secure the release of one of his clients in a prisoner swap with Turkey, and over his dealings with Ukraine.

One incident occurred when the former New York mayor was representing Reza Zarrab, an Iranian Turkish gold trader accused of helping a state-owned Turkish bank funnel more than $10bn worth of gold and cash to Iran in defiance of US sanctions.

In an Oval Office meeting in 2017, Giuliani pushed for Zarrab to be released as part of a potential prisoner swap with Turkey, the New York Times reported on Friday.

There was a swift objection from Rex Tillerson, then secretary of state, “who argued that it would be highly inappropriate to interfere in an open criminal case, according to two people briefed on the meeting”, the paper added.

Giuliani, who was not yet Trump’s lawyer, did not accept Tillerson’s objection and continued to argue. “Rather than side with his secretary of state, Mr Trump told them to work it out themselves, according to the two people briefed on the meeting,” the paper said. The prisoner swap did not take place.

Separately, the New York Times reported that federal prosecutors in Manhattan are investigating whether Giuliani broke lobbying laws in his dealings with Ukraine.

The investigation is reportedly connected to the case of two Giuliani associates who have been charged with campaign finance violations for channeling foreign money into Trump’s campaign.

Giuliani has emerged as a central figure in the impeachment scandal triggered by Trump’s phone call with the president of Ukraine, in which he requested an investigation into Joe Biden, his potential opponent in next year’s election.

The former New York mayor had been pushing Ukrainian officials to investigate Biden’s son, Hunter. This week two of Giuliani’s associates in that effort were arrested on charges of violating federal campaign finance laws.

A whistleblower complaint, which sparked the formal impeachment inquiry against Trump, refers to Giuliani 31 times. It paints a picture of a lawyer who in the service of his old friend and now personal client – Trump – allegedly circumvented national security protocols as he travelled between Washington and Kyiv carrying private orders from the president, many of dubious legality.

A separate report by the Bloomberg agency this week said Trump pressured Tillerson to help persuade the justice department to drop a criminal case against Zarrab. “Tillerson refused, arguing it would constitute interference in an ongoing investigation of the trader,” according to Bloomberg.

“Tillerson immediately repeated his objections to then-Chief of Staff John Kelly in a hallway conversation just outside the Oval Office, emphasizing that the request would be illegal,” the report said.

Giuliani told Bloomberg earlier this month: “Suppose I did talk to Trump about it – so what? I was a private lawyer at the time. Maybe I’m wrong. Maybe at some point I dropped his name in a conversation. Or maybe one of his people talked to him about it because I was trying to do a prisoner swap.”

And in an interview with the New York Times, he compared his efforts to the spy exchanges that took place during the cold war. “It happened to be a good trade,” he said. “I expected to be a hero like in a Tom Hanks movie.”

Ed Pilkington contributed to this report