Nicola Sturgeon has said difficulties obtaining visas for overseas artists has “undermined” the prestigious Edinburgh International Book Festival, and she demanded: “The UK Government needs to get it sorted.”

The Scottish First Minister – a keen reader who is also taking part in the literary event – hit out after book festival director Nick Barley said some of the writers had been “humiliated” by the measures they had to go through to get permission to enter the country.

He also warned the UK’s reputation as a global arts venue could be seriously damaged if problems in obtaining visas worsen after Brexit.

Mr Barley said one author had had to supply his marriage certificate, his daughter’s birth certificate and bank statements, before then being sent for biometric testing, in order to get his visa

The festival director told BBC Radio Scotland the author concerned “was so humiliated by that he decided he didn’t want to go through with the process of coming to Edinburgh to talk”.

He added: “I persuaded him to stick with it and thankfully we got the visa, but this is just one example of the kind of crazy things people are being made to do in the name of coming to talk about their books.”

Speakers at the book festival this year include Chelsea Clinton, the daughter of former US president Bill Clinton and his wife Hillary, who was the first woman to run for the White House, as well as Labour leader Jeremy Corbyn, and former prime minister Gordon Brown.

The literary celebration is due to get under way on Saturday, but Mr Barley said they are still to get visas for four people scheduled to take part.

He raised the issue after musician Peter Gabriel said it was “alarming” that a number of artists were unable to perform at his world music festival Womad in Wiltshire after they faced visa issues.

Mr Barley said it is an “increasing problem” for guests to have issues getting the necessary permissions, with 12 authors having faced “serious problems” this year.

“We’ve managed to overcome nearly all of them,” he said. “We’ve got four outstanding, and I think we will resolve them with any luck.

“But I think if this goes further we start to damage the reputation of the festivals, and we start to have authors wondering whether they can be bothered to go through that process of applying to come.”

While he said senior government officials in both Edinburgh and London had been trying to help, along with ambassadors and members of the British Council, he claimed: “I think the immigration laws which have been set in the last few years have had this consequence on artistic travelling.”

Most of those who have had difficulties this year have been authors from the Middle East and parts of Africa, he said, adding: “I foresee after Brexit we may have similar issues with authors and musicians coming from Europe. If that happens then we do seriously damage our chances of putting on a genuinely international festival.”

Ms Sturgeon commented on Twitter, saying: “It is really not acceptable that one of the world’s most renowned and respected book festivals @edbookfest is being undermined in this way. The UK government needs to get it sorted.”

A Home Office spokesman said: “We welcome artists and musicians coming to the UK from non-EEA countries to perform.

“In the year ending December 2017, 99% of non-settlement visa applications were processed within 15 days and the average processing time in 2017 was just under eight days.

“Guidance on visa and entry clearance requirements is publicly available on gov.uk. Each case is assessed on its individual merits against the published immigration rules.”

Maria Alyokhina of the protest punk band Pussy Riot should be in Edinburgh to take part in both the book festival and the Edinburgh Festival Fringe, despite being barred from leaving Russia.

The Pussy Riot team said: “In defiance of yesterday’s Russian authorities’ ban on her travelling, Pussy Riot founder Maria refused to be captive and silenced and instead has driven over 1,000km from Moscow through the night and boarded a flight.

“She was absolutely determined to perform the show at Summerhall and will be there in person to join her band-mates to share her story.”