Mr Tewari said the allegations of bribery were "very serious" and said Narendra Patel had alleged that Gujarat BJP President Jitubhai Vaghani was the culprit.
"It calls for reaction from the Prime Minister and the BJP President. It calls for registration of FIR against the Gujarat BJP. It calls for investigation under a sitting judge of the Gujarat High Court. If this is not checked, the sanctity of the election process in Gujarat in times to come will be questioned," Mr Tewari said.
He said it was incumbent on Prime Minister Narendra Modi to investigate the allegations as these were being levelled against his own party leaders.
He also accused the BJP of trying to "break" people-led movements opposed to BJP rule in Gujarat.
"Why is the BJP trying to coerce, lure, allegedly bribe the leaders of this movement and trying to break it? Isn't this a clear sign of their frustration? Isn't this a clear manifestation of their demoralisation?" he asked.
He said "allegations of bribery" were also levelled by Congress MLAs during the Rajya Sabha election earlier this year.
"Congress MLAs were coerced, attempts to bribe them were made, every instrumentality of state and central government was used and misused by the BJP-led central government. Income Tax, Enforcement Directorate and god knows which other agency was tasked to raid the resort where the MLAs were staying in order to protect themselves."
He said the truth prevailed in the end and the BJP lost the Rajya Sabha poll.