Photograph: Manuel Balce Ceneta/AP© Provided by The Guardian Photograph: Manuel Balce Ceneta/APA thinktank linked to the Orbán government, the Centre for Fundamental Rights, has issued an invitation to Trump, a government source told The Guardian.

The invitation comes as Orbán moves into campaigning mode ahead of a closely fought election due on 3 April, when his Fidesz party will face a united opposition coalition, in what is seen as the biggest challenge to his rule since he became prime minister 12 years ago.

Related: Phones of journalist who tracked Viktor Orban’s childhood friend infected with spyware

“People in Fidesz would really like Trump to visit Budapest in March,” said the source, who added that Trump has not yet replied to the invite. If it happens, the visit would be Trump’s first known trip outside the US since he lost the elections in 2020.

Orbán was an early Trump supporter, endorsing him as early as summer 2016, and he also publicly backed him in the 2020 vote. The pair spoke by telephone in January, and Trump returned the favour, publicly endorsing Orbán for the April election. An in-person visit by the former US president would be seen as a major campaign boost.

“These visits have a huge influence in the Hungarian conservative community, because they see [Trump] as an icon, as someone who spent his presidency in a strong headwind,” said a source close to Fidesz.

One former Republican staffer said Trump is known to fear contracting Covid while travelling abroad and may prefer not to travel.

Liz Harrington, chief spokesperson for Trump, did not respond to a request for comment. Asked to comment on various aspects of the invite, Orbán’s spokesman Zoltán Kovács responded with one word: “Nope.”

It is likely that Trump has been invited to the Conservative Political Action Conference (CPAC), due to be held from 25-26 March in Budapest. It will be the first time a European country hosts the flagship conservative event.

Miklos Szanthó, the director of the Center for Fundamental Rights, told the Hungarian news agency MTI that a number of US senators would attend the conference, as well as Santiago Abascal, the leader of Spain’s Vox party and Jair Bolsonaro’s son Eduardo.

Fidesz is hoping that Trump will join Orbán as the event’s keynote speaker, the Hungarian government source said.

“According to our plans a number of high profile Americans will attend CPAC Hungary, including politicians, as well as prominent thinkers and opinion leaders on the right. We are certain that any fresh information regarding guests and speakers will reach you in due course of time,” said Szanthó.

The thinktank’s mission statement says it acts as a “counter against today’s overgrown human rights fundamentalism and political correctness”. It is known for echoing the government’s communications and creating propaganda videos. According to research by the investigative Hungarian news outlet, Átlátszó, almost all of their budget is provided by grants financed from public funds.

Trump and Orbán met during a 2019 White House visit, when Trump said the two men were similar: “You’re respected all over Europe. Probably a bit like me, a little bit controversial, but that’s OK”.

David Cornstein, a long-time friend who Trump appointed ambassador to Hungary, said Trump admired Orbán for his strongman image and his control of the Hungarian political scene: “He would love to have the situation that Viktor Orbán has,” Cornstein said in 2019.

After Trump left office, Orbán’s relations with Washington soured, and Hungary was the only EU nation not invited to Joe Biden’s recent Democracy Summit. Relations with the Trump camp have remained strong.

Related: How Tucker Carlson and the far right embraced Hungary’s authoritarian leader

In September, former vice-president Mike Pence spoke to a conference on conservative social values hosted by Orbán. Former attorney general Jeff Sessions was also a recent visitor.

Fox News host Tucker Carlson also spent time in Hungary earlier this year, broadcasting several shows from Budapest and making a “documentary” that painted Hungary as a conservative paradise, under constant attack by the Hungarian-born billionaire, George Soros.

It was Carlson’s second trip to Hungary in less than a year. Last August he travelled to Budapest to interview Orbán. A few weeks after the Hungarian PM’s appearance on Fox, Trump sent him a letter of congratulations: “Great job on Tucker, proud of you!”Viktor Orbán invites Trump to Hungary to boost re-election campaign (msn.com)