Switzerland's ambassador to Iran on Thursday faced accusations of betraying the women-led protest movement after she wore all-enveloping black Islamic dress on a visit to a holy shrine alongside clerics.

The Swiss foreign ministry has batted away the criticism, saying ambassador Nadine Olivieri Lozano was appropriately dressed in line with protocol for a visit to a holy site.

Iranian media had published images of Lozano dressed head-to-toe in black with a full headscarf and long black garment alongside turbaned clerics during a visit to the holy shrine city of Qom.

The visit came more than five months into protests sparked by the death in custody of Mahsa Amini, a 22-year-old Iranian Kurd who had been arrested for allegedly breaching the country's strict dress code for women.

All Iranian women have been obliged since shortly after the 1979 Islamic Revolution to cover their heads and bodies, with the authorities consistently refusing to give ground on the rule.

Abolishing the obligatory headscarf has been one of the demands of the protest movement, along with the removal of the entire Islamic theocracy ruling the country.

"Swiss ambassador Nadine Olivieri Lozano wears a chador and goes to a mosque with the mullahs," said Belgian lawmaker Darya Safai, who has played a prominent role in rallies in Europe supporting the protest movement.

"While millions of Iranian women are fighting for women's rights and knowing that thousands have been killed for it, she wears a hijab and makes publicity for the oppressors. Disgusting!" she said on Twitter.

Actor and activist Nazanin Boniadi, who spoke in support of the protest movement at the Munich Security Conference at the weekend, said: "The Swiss ambassador in full conservative religious covering -- while brave Iranian women risk everything for freedom —- is exactly what you should not do."

Masih Alinejad, a US-based dissident who for years has led a campaign against the obligatory hijab, said the ambassador's dress choice was "shameful and (a) betrayal to Iranian women".

But the Swiss foreign ministry told AFP that "during the visit to the religious site, the applicable dress protocol for women was followed."

It added: "Interfaith dialogue is of great importance in the current context."

Foreign women, including dignitaries, are not exempt from Iran's dress rules and how to wear the headscarf has long been a dilemma for visiting VIPs.

But Boniadi said on Twitter: "If you don't normally wear a head covering by choice, at least avoid publicly documented displays of doing so while Iranian women are risking everything for (the) right to choose."

The ambassador of Switzerland is a key post as the Swiss embassy handles the interests in Iran of the United States, which has had no diplomatic relations with the Islamic republic since the aftermath of the revolution