The SUV of Sapotara MLA Ramesh Chand Meena, who is also a Parliamentary Secretary in Rajasthan government, was damaged in the incident, police said.
Kirori Meena, Dausa MP and a tribal leader, was scheduled to address a public rally organised by his supporters in the Bhankari village near Sapotara town, sources said.
Before Meena could reach, Ramesh Chand Meena arrived at the venue and was confronted by agitated supporters of the MP.
They asked him to go back and the arguments got heated, sources said adding, soon a scuffle broke out.
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Both sides accused each other of firing in the air to create panic, but the police didn't confirm it.
"Kirori Meena's supporters damaged my vehicle and beat my supporters.
His men also opened fire in the air and I will lodge an FIR against them," Ramesh Meena told PTI over phone.
An aide of Kirori Meena blamed Ramesh Meena's supporters for disturbing atmosphere in the meeting.
"It was a public meeting of Kirori Meena, but Ramesh Meena arrived uninvited.
When our supporters asked him to go back, he became adamant and his supporters started the trouble and even fired in the air," he said.
Sources said, after the interruption, the meeting went on peacefully.