Organisers of Miss Universe extended their "deepest apologies" to India over a photo shoot at the Taj Mahal that triggered a police case and accusations that she disrespected the famed monument to love.

Reigning Miss Universe Olivia Culpo, a 21-year-old American from Rhode Island, visited the Islamic mausoleum on Sunday during a 10-day tour of India.

During her time at the World Heritage site, she posed for cameras with branded shoes and sat on the Diana Seat, a marble ledge named after the late British princess who visited in 1992.

Acting on a complaint from the site's caretaker, police filed a case because any advertising or promotional work is banned at the site.

"The Miss Universe Organization would like to extend its deepest apologies to the people of India for the incident involving the reigning Miss Universe," said a statement sent to AFP late Thursday.

It said Culpo was making a video diary for fans. "As part of these videos, we sometimes incorporate sponsors into these shoots," it said, adding the footage was not meant for commercial purposes.

"We sincerely apologise for any unintentional harm our indiscretion and insensitivity may have caused," it added.

Indian-born fashion designer Sanjana Jon, who accompanied Miss Universe to the site, has also been booked for an alleged breach of the Ancient Monuments and Archaeological Sites and Remains Act.

They are likely to face a fine if found guilty, officials say.

The Taj, visited by millions of tourists each year, was built by Mughal emperor Shah Jahan as a tomb for his beloved empress, Mumtaz Mahal, who died during childbirth in 1631.

Visitors are asked to remove shoes while climbing the plinth and entering the Taj, but footwear is allowed in the surrounding garden area where Culpo posed, wearing a long peach-coloured off-the-shoulder dress.

The Mumbai-based Mid-Day tabloid quoted Taj caretaker Munazzar Ali earlier this week as saying Culpo's behaviour amounted to "disrespect and insult".

"The sandals from a bag she carried were taken and placed on the Diana Seat for shooting pictures, which is not permitted by the ASI (Archaeological Survey of India). It also amounts to disrespect and insult," he told the paper.

The tabloid suggested that security personnel responsible for frisking at the entrance gates "were too impressed" with Culpo and allowed her to carry her bag inside, which is normally not permitted.

Culpo, seemingly unaware of any brewing controversy, uploaded a photo of the Taj to an Instagram account on Monday, a day after her visit to the Taj in Agra, a three-hour drive south of the capital New Delhi.

"We made it to the Taj Mahal. One of the most beautiful places I've ever seen!!!! So amazing,"