The unexpected move cast doubts over talks between India and Pakistan and sent stock prices falling.
The president of the Congress party, Sitaram Kesri, citing what he called growing lawlessness and a drifting economy, told President Shankar Dayal Sharma that his party could no longer offer make-or-break backing for Mr Deve Gowda's centre-left government.
Mr Kesri staked a claim to form a new government led by Congress, which finished a humiliating second in general elections last year behind the Hindu nationalist Bharatiya Janata Party (BJP).
The ruling United Front alliance said that Mr Deve Gowda would not resign but would face parliament when it reconvenes on 21 April. "There is no question of the resignation of Mr Deve Gowda," Jaipal Reddy, a spokesman for the United Front, said.
The decision by Congress to try to topple the minority government coincided with the third day of peace talks between Indian and Pakistani diplomats in New Delhi. The negotiations began on Friday after a three- year impasse provoked by deep differences over the divided Himalayan region of Kashmir.
Rival Indian politicians agreed that their domestic rumpus would have no impact on the dialogue with Pakistan. But the political upheaval appeared to add another complication to the fragile dialogue between the two countries, which have been at war three times since their independence from Britain in 1947. Two of the conflicts were over Kashmir. The high stakes in the talks were underscored by renewed violence in the Indian state of Jammu and in Kashmir.
Nor was it clear whether Congress, with 140 deputies in the 545-seat lower house, could muster enough support to run a new coalition. Waiting in the wings was the BJP, which, with its supporters, controls 194 votes.
The BJP said Mr Deve Gowda's government was a disaster and Congress's proposed experiment would prove catastrophic. "One experiment collapsed, the other may not take off," it said.