With one music video, Justin Bieber has made a pristine Icelandic canyon famous around the world. And that’s the problem.

Icelandic environmental officials have had to close off Fjaðrárgljúfur to protect it from the hordes of Bieber fans who are determined to visit the site, which is featured in the video for I’ll Show You. But these fans are not letting a few fences, signs or park rangers keep them away.

I’ll Show You by Justin Bieber

It’s just one example of the challenges to Iceland’s fragile environment posed by its growing popularity with international visitors.

Last year 2.3 million tourists visited the North Atlantic island nation, compared with 600,000 eight years ago. The 20% annual rise in visitors has been out of proportion with systems needed to protect Iceland’s volcanic landscape, where soil forms slowly and erodes quickly.

Guðmundur Ingi Guðbrandsson, the environment minister, said it was “a bit too simplistic to blame the entire situation on Justin Bieber” but urged famous or otherwise influential visitors to consider the consequences of their actions.

“Rash behaviour by one famous person can dramatically impact an entire area if the mass follows,” he said.

Eager visitors have tried to sweet-talk the ranger Hanna Johannsdottir into opening the gate. Some offer bribes, she said, but they should know in advance it is not going to work.

“Food from people’s home country is the most common bribery,” said Johannsdottir, who recently turned down a free trip to Dubai in exchange for looking the other way at trespassers.

“We came because of Justin Timberlake,” said Mikhail Samarin, a tourist from Russia, travelling with Nadia Kazachenok and Elena Malteseva, who were quick to correct the artist’s last name to Bieber.

“It was so amazing,” said Malteseva about the Bieber video. “After that, we decided it was necessary to visit this place.”

The three took turns posing for a photograph, standing at the edge of a cliff.

The video has been watched more than 440m times on YouTube since Bieber stomped on mossy vegetation, dangled his feet over a cliff and bathed in the freezing river underneath the sheer walls of the canyon.

“In Justin Bieber’s defence, the canyon did not – at the time he visited – have rope fences and designated paths to show what was allowed and what was not,” Guðbrandsson said.