Their accomplice Barkat Ali fled after learning about the police raids, said Jodhpur police commissioner Sachin Mittal.
Another youth, whose identity was not revealed, was picked up for questioning from Jamia Nagar in the capital, as he had been in touch with the Rajasthan trio.
Rehman was visiting the state to oversee the preparations being made by the Rajasthan module for a terror strike, the police officer said.
"A huge amount of explosive materials such as detonators, timers, circuits from the residence of these three people. With this, a spectacular terrorist strike has been averted," the commissioner said.
Were Modi, any politician or election meetings a target of this module?
"Investigation so far doesn't point towards it. Any important event including elections can be targeted, but we are at a very preliminary stage of investigation and I would not like to speculate as of now," he said.
A close aide of jailed IM co-founder Yasin Bakhtal, Rehman is wanted in terror strikes in Mumbai, Jama Masjid, Pune and Hyderabad and Bodh Gaya.