Mr Mishra did not name Mr Gandhi, but said political leaders will have to wait for a few days before they can plan visits to Saharanpur, about 181 km from national capital Delhi.
"Congress Vice President Rahul Gandhi has not been given permission to visit Saharanpur," news agency Press Trust of India quoted another senior police officer Bablu Kumar as saying.
Congress sources in Delhi however said on Friday afternoon that they have received no word on Mr Gandhi being denied permission and said his trip on Saturday is on. The Congress leader plans to visit Shabbirpur village, the epicentre of clashes between Dalits and Thakurs or Rajputs since last month.
On Tuesday, a Dalit man was killed and several people were injured when a mob attacked supporters of Bahujan Samaj Party leader Mayawati with swords and guns soon after she held a rally in Shabbirpur. Before Ms Mayawati's rally 12 homes in the village belonging to Rajputs had been set afire by unknown people and the mob attack was seen as retaliation. Groups of Dalits then attacked shops and markets.
The Yogi Adityanth government of the BJP in UP has blamed Ms Mayawati's visit and has called the continuing incidents of violence in the area a "well-planned conspiracy."
Chief Minister Adityanath despatched a team led by the states home secretary to Saharanpur the same night by special plane and the Union Home Ministry has rushed 400 riot-control policemen to ensure law and order Saharanpur. Mobile internet services and social networking sites were blocked in areas where there have been clashes, to prevent the spread of rumours.
UP's Deputy Chief Minister and state BJP president Keshav Prasad Maurya has accused Ms Mayawati of funding the Bhim Army, a regional outfit that the government alleges has instigated the clashes. The governmnet said its leader Chandrashekhar Azad is likely to be arrested.
Ms Mayawati has denied any links with the Bhim Army and said it was using the name of Dalit icon Babasaheb Ambedkar and the BSP to exploit the poor Dalits, who make up a big chunk of her party's support base.
Chief Minister Akhilesh Yadav of the Samajwadi Party has targeted the three-month-old Yogi Adityanath government, accusing it of "abject failure" in maintaining peace and law and order in the state.
The BJP swept the UP assembly elections in March this year, decimating the BSP and the Samajwadi Party-Congress alliance.