The police resorted to lathi charge to stop activists, numbering in hundreds, from marching towards the hill top through the Meera Gate circle from Malanmasi Balaji temple, the official said.
About 10 to 12 persons including two sadhus who were leading the activists, were detained.
Kota divisional commissioner extended the suspension of internet services till 6 am on January 3 in the Bundi district to prevent further trouble.
Hindu Mahasabha and some other organizations had earlier given a call to perform Puja at Maandhata Balaji cenotaph on Tiger Hill on January 1, following which the district administration imposed prohibitory orders under section 144 on Friday night and the divisional commissioner ordered suspension of internet services from 6 am on December 31 to 6 am January 2.
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Police officials did not confirm the specific number of injured and those detained.
Amid the prevailing tension, a large number of tourists, foreign and domestic, who had moved to the city for New Year celebrations were forced to stay inside.
Some activists of Hindu organizations had given a call to perform worship on the Tiger hill adjoining the Meera Sahab Dargah which was against the decision of the Peace Keeping Committee, said Vishal Bansal, IG, Kota range.
There also has been opposition to the attempt to hold puja at the spot.
"We only object to starting a fresh tradition of Puja on the Tiger hill which has a common way to both the dargah and Maandhta cenotaph. If the tradition of Puja is started, it will continue create tension in the city which is known its communal harmony," said a local.