The fight began later that day outside Mehrangarh fort, the venue for a dinner, after a security guard slapped a television reporter as journalists tried to chase the celebrity couple's car into the fort.
Angry journalists then broke through one of the security cordons, setting off a fistfight with security guards that lasted nearly an hour. No serious injuries were reported.
Police and organizers of the event declined to comment on the incident, the AP said.
Hurley and Nayar were expected to fly out of the city later Saturday, and about 50 police constables were deployed at the airport.
The dinner followed the celebrity couple's Indian wedding earlier in the day at Umed Bhavan, a massive sandstone palace turned into a luxury hotel.
It was their second wedding in a week. The couple was first wed in a private civil ceremony in a castle outside London.
Security around the wedding functions have been intense. A team of security guards flown in from London were bolstered by another 50 guards from Mumbai.
Actress Hurley appeared in "Austin Powers: International Man of Mystery" and "Bedazzled," and for several years was the international face of Estee Lauder cosmetics. Her 4-year-old son, Damian, accompanied the couple on their trip to India.
Putin's official spokesman Dmitry Peskov commented on remarks in the US media about failures in launching nuclear-capable missiles in Russia
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