PORT LOUIS (Reuters) - Mauritius police said on Monday it had stepped up security after gunshots were fired at the French embassy and a hotel in the capital city.

A police official said nobody had been injured and an inquiry had begun to identify and apprehend the perpetrators, adding graffiti mentioning the Islamic State in Iraq and Syria (ISIS) was discovered on the wall of the French embassy.

"Police attended a request early in the morning in St Georges street and found traces of projectiles on the bay window of St Georges Hotel and a window found on the ground floor of the French embassy," police commissioner Mario Nobin told reporters.

He said the security level had been raised in the country, but described the situation on the Indian island nation as under control.

Mauritius says ISIS has no presence on the island.

Muslims, who make up nearly a fifth of Mauritius' 1.2 million people, have lived peacefully with majority Hindus and Christians since the former British colony obtained independence in 1968.