All BJP lawmakers will participate in the fast, which includes members of PM Modi's council of ministers.
"The people who couldn't gain power in 2014, don't want the country to move forward".
The parliament could barely work for an hour on each working day.
Shah will hold a "dharna" (sit-in) in Karnataka's Hubli, it added.
According to media reports, Home Minister Rajnath Singh would fast in Lucknow and Roads Minister Nitin Gadkari in Nagpur. Attempts are being made to make the movement of this fasting act universal, as hashtag Fast with Modi began to trend quite early in the morning, with people being asked to change their display picture to a note, that said, "I am on Fat on 12th April". "This version was prepared before Prime Minister Modi's fast was announced", a PMO source said. Tourism Minister KJ Alphons will observe the fast in Kerala.
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He said the observance of fast by Modi and BJP MPs was an attempt to divert attention of the nation from burning issues such as agrarian distress, rising unemployment and bungling in the implementation of GST. Nirmala Sitharaman will observe the fast in Chennai; Prakash Javdekar in Bengaluru; Vijay Goel in Tamil Nadu and KJ Alphons will fast in Kerala.
The Prime Minister's decision to hold a fast came after Congress President Rahul Gandhi observed a day-long fast at Rajghat in New Delhi on April 9 over alleged atrocities on Dalits, Adivasis, and minorities.
The opposition Congress termed the fast by the Prime Minister as a "farce" and said he should apologise over the way his party had "denigrated and disrespected" parliament. Modi also lauded government officials, including IAS officers, for doing excellent work on the sanitation front.
Parliament couldn't function for the entire 22 days of the second part of the Budget session due to the commotion in both Houses.
Addressing party MPs through an audio conference call ahead of the protest, Modi said the BJP leaders and its workers will observe the fast on Thursday to "expose" those handful of people who "throttled" democracy by stalling Parliament proceedings during the budget session.