"I will not ask the Shettar government to prove majority because there is no threat to it from the 13 assembly members who intend to quit," Bhardwaj told reporters on the margins of the Republic Day function here.
The 13 assembly members of the ruling Bharatiya Janata Party are loyalists of party's former leader B.S. Yeddyurappa and have been waiting since Wednesday for Speaker K.G. Bopaiah to submit their resignations.
Bopaiah, who has been out Bangalore since late Tuesday, is expected to resume work Jan 28 or 29 when the resignations would be submitted to him.
Bhardwaj said he would decide the next course of action if their resignations were accepted by the speaker.
He said there was "no constitutional crisis as of now" but "I will watch the develpments day-by-day, minute-by-minute".
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Bhardwaj said he would address the joint session of the legislature as scheduled on Feb 4. The budget session is to end Feb 13.
"Each day of the budget session is a test for government," the governor said, in an apparent reference to efforts of by Yeddyurappa and his supporters in BJP to bring down the Shettar government to prevent the chief minister from presenting the budget for 2013-14 on Feb 8.
Shettar, who also attended the function, maintained that he enjoyed majority and there should not be any doubt over whether he would present the budget or not.
The BJP has 118 members, including the speaker in the 225-member assembly which has one nominated member.
The resignation of the 13 legislators would bring down the party's strength to 105. It has support of one Independent who is a cabinet minister.
The Congress has 71 members and the Janata Dal-Secular 26. There six other independents and two seats are vacant.