Zameer Ahmed Khan had said it was not possible to reach the post with support from one community.
A Congress leader in Karnataka, belonging to the Siddaramaiah camp, has been strongly reprimanded by the party leadership for his "Muslims outnumber Vokkaligas" comment, which had stirred up a huge political controversy in the state ahead of next year's assembly elections.
Zameer Ahmed Khan, reacting to Mr Siddaramaiah's arch-rival DK Shivakumar's chief ministerial aspirations, had said it was not possible to reach the post with support from only one community.
After a day of firefighting, a letter from Congress spokesperson and senior leader Randeep Surjewala warned Mr Khan to be "careful" and adhere to the party line.
"Your recent public remarks are unwarranted and in poor taste...and ended up creating unnecessary faultlines," Mr Surjewala wrote.
"The foundational ideology of the Indian National Congress is its inherent inclusiveness, away from the divisions of caste and religion. No member of the Congress party should make any remarks or statements against the grain of this all-encompassing thought that runs through our veins," the letter added.
Mr Khan had hit back after Mr Shivakumar, a member of the politically powerful Vokkaliga community, had sought support to reach his goal.
"No one can become CM with support from one community, everyone will have the desire (to become CM) that's not wrong...it is possible (to become CM) only by taking all communities together? I too have a desire to become CM, my community's percentage is more than that of Vokkaligas. Is it possible for me to become CM, just with the support of my community? Not possible," Mr Khan had said.
Vokkaliga leaders from the state's ruling BJP had ripped into Mr Khan, dubbing his remarks an attempt to belittle the community. Reports said Nirmalanandanatha Swami, a prominent Vokkaliga seer, has conveyed his unhappiness to Congress leaders.
Karnataka is one of the few states where the Congress is comparatively strong. But another bout of infighting has surfaced ahead of next year's assembly elections over the top post in case the party wins. While former Chief Minister Siddaramaiah is a strong contender, the party's state unit chief DK Shivakumar has made the first overt move.