The difference of opinion among the legislators surfaced in a meeting convened by Kumaraswamy on Friday night to decide the party's future course of action.
GT Devegowda, a JD(S) lawmaker and former minister, has said that a few party MLAs have impressed on former CM HD Kumaraswamy to extend external support to his successor BS Yediyurappa who took oath as the chief minister of Karnataka for the fourth time on Friday.
He, however, added that only Kumarswamy would take the final call, PTI reported.
The difference of opinion among the legislators surfaced in a meeting convened by Kumaraswamy on Friday night to decide the party's future course of action in the wake of upheavals in Karnataka politics.
After the meeting of party legislators, Devegowda said, "We (MLAs) discussed the future course of action. Some have suggested that we should sit in opposition, while some legislators are of the opinion that we should support the BJP from outside."
"We have authorised Kumaraswamy to take the final decision," he said.
The development came on a day when BJP leader B S Yediyurappa was sworn in as a chief minister in a sudden twist to the protracted high political drama in the state with a big challenge to manage numbers staring him in the face.
Shortly after taking the oath, Yediyurappa said he would move a motion of confidence in the Assembly on July 29, to prove his majority.
Yediyurappa alone took the oath succeeding Kumaraswamy three days after the Congress-JDS coalition government crumbled under the weight of a rebellion by a big chunk of its lawmakers when it lost the motion of confidence in the state assembly.
The JD(S) and its ally in the previous government -- the Congress -- had alleged that the BJP was the root cause behind unseating them from power by luring and threatening their MLAs.
Meanwhile, JD(S) patriarch and former prime minister H D Deve Gowda, in a tweet, congratulated Yediyurappa on his swearing-in.
Amid speculations about BJP and JD(S) joining hands, Yediyurappa had recently ruled out any possibility of an alliance with the regional party, having bitter experience in the past.
The BJP and JD(S) had formed a coalition government in 2006 with Kumaraswamy as chief minister and Yediyurappa as his deputy, under a power-sharing formula of 20 months each.
That government had collapsed as the JD(S) did not transfer power to BJP, paving the way for the saffron party to win elections in 2008.
(With inputs from PTI)