"Kumaraswamy will not resign today," state unit JD-S President Merajuddin Patel told reporters, rejecting the saffron party's demand.
As per the power-sharing pact, JD-S is supposed to transfer power to BJP on October three.
In a significant statement that would further precipitate crisis between the partners, JD-S disowned the power sharing agreement saying it was reached between Kumaraswamy and the BJP, and JD-S has nothing to do with it.
"We have nothing to do with power sharing agreement reached between Kumaraswamy and BJP 20 months ago," Patel
said, indicating that JD-S will not honour the pact.
JD-S supremo H D Deve Gowda said this morning the party's Political Affairs Committee scheduled to meet in Delhi on October five will take a final decision on power transfer, in an indication that his party will not accept "this evening" deadline.
Kumaraswamy, meanwhile, told reporters here he did not want to take any decision on the issue in a "haste".
"It is better these decisions are not taken in a haste. Such a step will not be in the interest of both the parties," Kumaraswamy, who has also struck a defiant posture on the power transfer issue, said.
Kumaraswamy is expected to elicit views of his party MLAs later on Tuesday on the power transfer.
The BJP, meanwhile, stuck to its deadline that Kumaraswamy should resign by this evening.
"October three is the deadline for power transfer. We will not go back on that. October five (the date JD(S) says it will take a final decision at its political affairs committee meeting) does not come into the picture at all," the party's state unit president D V Sadananda Gowda said in Bangalore.
Asked about BJP's stand if Kumaraswamy does not resign on Tuesday, he said: "Let's see tomorrow".
The BJP has convened a meeting of its legislature party later on Tuesday to take stock of the situation. Party MPs and office bearers have been invited for this interaction.
At a meeting on Monday, BJP ministers decided to stand firm on the power transfer issue and spoke against allowing Kumaraswamy to continue as Chief Minister beyond October 3.
The JD(S), meanwhile, also sought to draw attention to the power sharing agreement between the Congress and Mufti Mohammed Sayeed's party in Jammu and Kashmir, saying handing over the reins to Ghulam Nabi Azad was delayed after "people wanted the former to continue".
Kumaraswamy took a swipe at BJP leaders who have been talking through "media" and cautioned them that this kind of behaviour would only worsen the situation.
Calling for a halt to the "dialogue through media", he exhorted saffron party leaders to hold talks with his party leaders to resolve the crisis.
"Yashwant Sinha has said that I should resign by this evening and give a letter of support to Governor. I have read this only in the media. No one told me directly", he said.
Kumaraswamy advised the BJP to have "patience" and give time to his party to decide the issue.
"Why are they in such a hurry?" he asked.
The Chief Minister also referred to the delay in power transfer in Jammu and Kashmir from the PDP to the Congress.
There was a three-month delay in transition of power in Jammu and Kashmir.