The issue is more of an internal EU battle than a genuine dispute with the US, but risks harming relations.

Under EU law, the European Commission was obliged to impose US visas in April 2016 because the US continues to deny visa-free travel to people from Bulgaria, Croatia, Cyprus, Poland, and Romania on security gorunds.

The Commission did not do so for fear of causing a US backlash, however.

It told the Reuters news agency on Thursday that it was still in talks with US officials and would "report on progress before the end of June”.

MEPs are angry that the Commission did not follow due process.

A parliament source said they might take action at the EU court in Luxembourg if it continued to ignore their appeals.

If the Commission adopted the US visa decision, it would anyway be likely struck down by the parliament and by member states, both of which are keen to avoid a US visa war.

Istvan Ujhelyi, a Hungarian centre-left MEP, who co-chairs the parliament’s transport committee, said ahead of Thursday’s vote that “pragmatic internationalism must prevail over procedural rigour” in EU relations with US president Donald Trump.

“The effect of terrorism in Europe in recent years emphasised how fragile our appeal is as a destination in long-haul markets,” he added.

The European national tourist bodies’ lobby, the ETC, said the same, adding that €51 billion a year of spending by US visitors to the EU was at stake.

Trump has not remarked on the visa dispute, but he recently upset France by saying that Paris was no longer a nice place to go due to the terrorist threat.

Some experts, such as Andras Simonyi, a scholar of transatlantic relations at Johns Hopkins University in Washington, have also warned EU institutions not to antagonise the thin-skinned US leader.

“Don’t pull the lion’s tail,” Simonyi, who negotiated Hungary's US visa waiver in his previous post as Hungary's ambassador to the US, told EUobserver.