By Isla Binnie

ROME, Sept 22 (Reuters) - Rome is reopening its famed Spanish Steps after a privately funded restoration but has urged visitors to treat the 18th century staircase with greater respect to prevent it falling again into disrepair.

The site of one of cinema's most famous ice cream breaks in the film "Roman Holiday" has been largely shut since last October while technicians cleaned and repaired the monument.

Roman jeweller Bulgari paid 1.5 million euros ($1.7 million) to spruce up the 135 steps, which had become loose, stained and cracked under the strain of daily use by city-dwellers and hordes of selfie-snapping visitors.

The steps where Audrey Hepburn met Gregory Peck in the 1953 film underwent both chemical and mechanical cleaning. Large pieces of stone were added in some places and invasive weeds were removed from the balustrades.

Standing halfway up the staircase which joins Piazza di Spagna to the Trinita dei Monti church, Rome mayor Virginia Raggi said she had ordered police to monitor more closely people's behaviour on the steps and to stop anyone "camping out" there.

"I think it is essential to let people use these assets and also make them feel responsible for that use," Raggi said, adding "this use has often become abuse".

Bulgari is one of several companies to have responded to Italy's call for private investors to help prop up monuments whose condition has deteriorated after years of spending cuts.

Paolo Bulgari, great-grandson of the jeweller's founder, caused controversy this month when he proposed fencing off the steps to help preserve the expensive restoration from "barbarians" who have left them strewn in the past with chewing gum, coffee and wine stains.

But Bulgari chief executive Jean-Christophe Babin said he was confident the steps, which are a few metres from the brand's flagship store, would be better looked after in future.

"I walk there myself virtually every day to go the store and I have an eye on the steps - not to check, but just to admire," he said.

($1 = 0.8903 euros)

(Reporting by Isla Binnie; Editing by Gareth Jones) ((isla.binnie@thomsonreuters.com; +39 06 8522 4392; Reuters Messaging: isla.binnie.thomsonreuters.com@reuters.net))