By Philip Pullella

ROME (Reuters) - The head of one of Venice's most prestigious museums apologized on Wednesday to a Muslim woman asked to leave the building by a guard because she was wearing a veil over her face.

The episode, which has kindled controversy in the Italian media and arguments between centre-left and centre-right politicians, occurred on Sunday in Venice's Ca' Rezzonico museum, which houses 18th-century Venetian art.

"I'm sorry for what happened and if she ever wants to return to our museum, she will be more than welcome," director Filippo Pedrocco told Reuters by telephone from Venice.

The woman, visiting the museum with her husband and children, had cleared security when she entered the building.

When she reached the second floor, a room guard told her she must remove her "niqab," which leaves only the eyes visible, or leave.

"The room guard was over-zealous. He should not have done it. She already passed security and his only duty was to guarantee the safety of the artwork in his room," Pedrocco said.

The woman was believed to have been a member of a well-off family visiting Venice from Saudi Arabia or a Gulf state.

She refused to take off the veil and left the building, which faces Venice's Grand Canal and houses works by such 18th century Venetian masters as Giandomenico Tiepolo.

Italian anti-terrorism laws dating from the 1970s ban the wearing of face coverings in public but they are rarely enforced in cases of Islamic veils.

Italian media reported that the guard, who Pedrocco said worked part-time and was employed by an outside security firm, would be disciplined and risked being fired.

However, the guard, whose name was not disclosed, was hailed as a hero by some in the Veneto region, where there has been tension between long-time residents and Islamic immigrants.

Senator Roberto Castelli, a member of the anti-immigrant Northern League, asked the justice minister to make sure the guard was not disciplined or sacked "for doing his duty and making sure the law was respected."

Giancarlo Gentilini, deputy mayor of the city of Treviso north of Venice, said the guard should be "given an award and not punished."

(Editing by Andrew Dobbie)