Up to seven bombs have ripped through the north western Indian tourist city of Jaipur, killing at least 80 people and injuring scores of others.

The city is a top tourist spot in India and is often frequented by overseas visitors.

The bombs were detonated in quick succession over just 12 minutes as people were doing their evening shopping.

One bomb exploded near Jaipur's best known tourist attraction, the historic Hawa Mahal or Palace of Winds.

Authorities in the state of Rajasthan have arrested one suspect but are yet to publicly blame anyone for the attack.

The Mayor of Jaipur, Ashok Parnami has appealed for people to remain calm.

"It is a very sorrowful incident," he said.

"Jaipur has been known for peace and harmony, there has been no such earlier incident here.

"This happened for the first time and the entire city of Jaipur is in a state of terror."

India's junior interior minister Sriprakash Jaiswal says the authorities will carry out a full investigation.

"We have found a powerful explosive, possibly RDX has been used," he said.

"We cannot name any outfit at present as this will be known only after the investigation is done.

"But it is for sure that some lethal outfit has committed this disgraceful act and we strongly condemn it."