The self-styled “misogynist influencer” Andrew Tate and his brother, Tristan, have left Romania on a private jet and are flying to the US after their travel ban was lifted, officials and local media have said.

The pair, who were arrested in Romania in 2022 and face trial on charges of rape, sex with a minor, people trafficking and money laundering, took off from Băneasa airport in Bucharest for Fort Lauderdale at 6am (4am GMT), airport officials confirmed.

Local authorities said prosecutors had approved the brothers’ request to travel. The anti-organised crime unit, Diicot, said the pair remained “under judicial supervision” and would have to “appear before the judicial authorities at every summons”.

It added that violation of the obligations imposed on them “may lead to a higher custodial measure”. Local media said the pair, who are dual British and US nationals, were expected to return to Romania in March for a judicial control court hearing.

The brothers are outspoken supporters of Donald Trump, and several members of the US president’s inner circle have spoken out publicly against their treatment, including Donald Trump Jr who described their detention as “absolute insanity”.

Elon Musk responded to a suggestion from Tate that he would “run for prime minister of the UK” by saying “he’s not wrong”, while one of Tate’s lawyers, Paul Ingrassia, is the White House liaison official for the US Department of Justice.

According to Ingrassia, the Tate brothers were “sacrificed on the altar of the Matrix under the banner of egregious crimes they never committed”. The US vice-president, JD Vance, has appeared on a pro-Tate podcast.

Andrew Tate, 38, a former professional kickboxer, and his brother, 36, had been under a travel ban since their arrest along with two Romanian women on charges of human trafficking, rape and forming a criminal gang to sexually exploit women.

Diicot launched a second inquiry in August into alleged crimes including forming an organised criminal group, human trafficking, trafficking of minors, sexual intercourse with a minor and money laundering.

The brothers were among six people taken into custody then, when authorities ordered them to be placed under house arrest. The Tates and their suspected accomplices have denied all of the charges against them in both cases.

The brothers are also wanted by UK authorities who have filed an extradition request over allegations of sexual aggression in a case dating back to 2012. A Romanian court has ruled that proceedings in Romania must be concluded first.

In a joint statement, four British women who allege they were sexually abused by Andrew Tate said they felt “retraumatised” when they found out he had left Romania.

“It is clear that he will now not face criminal prosecution for his alleged crimes in Romania,” the women said. “He will use it as an opportunity to harass further and intimidate witnesses and his accusers, and he will continue to spread his violent, misogynistic doctrine around the world.”

The women had warned last week that the US government might push Romania to ease their travel restrictions, and the Financial Times has said Washington raised the Tates’ case with Romanian authorities.

The women’s lawyer, Matthew Jury, told the BBC that they had been “the victims of the most horrible and horrific alleged crimes … And to see the most powerful man in the world support their alleged abuser is incredibly traumatising.”

The Romanian foreign minister, Emil Hurezeanu, confirmed that Trump’s special envoy, Richard Grenell, had spoken to him about the brothers’ travel ban at this month’s Munich Security Conference.

Hurezeanu said Grenell told him he was “interested in the fate of the Tate brothers”, but he said there was “no form of pressure, no threat” from the US side and that “things are perfectly clear as far as we are concerned”.

Romania’s prime minister, Marcel Ciolacu, has also denied that the US made any request to Bucharest regarding “the legal situation of well-known foreign influencers investigated by Romanian authorities”, either during the conversation or after it.

Tate has been banned from several social media platforms for misogynistic views and hate speech but has more than 10 million followers on X, where he promotes an ultra-masculine lifestyle that critics say denigrates women.

In its second case against the brothers, Diicot alleges they used the so-called “loverboy” method – convincing people they are in a romantic relationship – to force 34 women into making pornography that was sold online for almost $3m (£2.1m).

Diicot alleges one of the defendants forced a 17-year-old to produce pornography in Britain and Romania, creating profits of $1.5m, and also alleges that the defendant repeatedly had sexual relations with a 15-year-old.