Hungary’s Viktor Orbán offered to go to great lengths to help Vladimir Putin, telling the Russian leader “I am at your service” in an October call, it has emerged, prompting further scrutiny of Budapest’s ties to the Kremlin just as JD Vance arrived in the city.

Air Force Two landed in Budapest on Tuesday morning carrying the US vice-president and his wife, Usha Vance, as Hungary reaches the final, heated days of a hard-fought election campaign that has played out against a backdrop of scandals regarding the relationship between Budapest and Moscow.

On Tuesday, Bloomberg News said it had obtained a Hungarian government transcript of a call that took place between Orbán and Putin on 17 October, in which Orbán reportedly compared the relationship to that of a “mouse” standing ready to help the Russian “lion” as needed.

“Yesterday our friendship rose to such a high level that I can help in any way,” Orbán reportedly told Putin in the call. “In any matter where I can be of assistance, I am at your service.”

In an attempt to emphasise his point, Orbán was said to have made reference to one of Aesop’s fables in which a mouse who was earlier shown mercy by a lion goes on to free the same lion when it is netted by hunters. The remark drew a laugh from Putin, the transcript suggested.

Orbán, the rightwing populist who has sought to turn Hungary into what he calls an “illiberal democracy”, is the EU’s most Moscow-friendly leader, leading some critics to refer to him as Putin’s Trojan horse.

The most recent revelation heightens the questions that have swirled in recent weeks regarding the lengths that the US and Russia are going to in order to bolster Orbán as he trails in the polls.

Donald Trump has repeatedly endorsed Orbán, describing him as a “fantastic guy” and a “strong and powerful leader”, while his administration has dispatched Vance seemingly in an attempt to turn the tide on Orbán’s lagging campaign. Russian intelligence agencies, along with disinformation networks with links to Russia, are alleged to be working to sway the election.

As Hungarians prepare to vote at the weekend, most polls have suggested Orbán is facing an unprecedented challenge from Péter Magyar, a former top member of Orbán’s Fidesz party, raising the prospect that Orbán could be ousted after 16 years in power.

The prospect has mobilised rightwing leaders around the world, catapulting the election in this central European country of about 9.5 million people on to the global stage.

The election is also being closely followed across the EU. Last week, several leaders expressed outrage over leaked audio that appeared to capture Hungary’s foreign minister, Péter Szijjártó, telling his Russian counterpart, Sergei Lavrov, that he would work to amend the EU sanctions list to its liking.

In the call revealed on Tuesday, Putin reportedly praised Hungary’s “independent and flexible” stance on his war against Ukraine. “It is incomprehensible to us that such a balanced, middle-ground position only generates counterarguments,” said the Russian president, according to the transcript.

The call ended with the two leaders inquiring about one another’s health. “I exercise, I also ski. I know you play football,” the Russian president said, according to the transcript. “I try,” Orbán replied, drawing laughter from both men.

Orbán then thanked Putin for the call, saying goodbye to him in Russian, it was reported.