India's election authorities have demanded an explanation from a politician over remarks he made during an election meeting in western Gujarat.
The police said Mr Sheikh was planning to kill Mr Modi
The state's chief minister, Narendra Modi, allegedly commented on the 2005 killing of a man by police in Gujarat.
According to Indian media, at Tuesday's meeting Mr Modi appeared to have "justified" the killing.
In April, three top policemen were charged with the murder of Sohrabuddin Sheikh, a Muslim civilian.
They are alleged to have attempted to cover up the killing by claiming he belonged to an Islamic militant group.
Mr Modi's Hindu nationalist Bharatiya Janata Party (BJP) government then admitted that the missing wife of Mr Sheikh, Kausar Bi, was also killed and her body was burnt.
A human rights group Citizens for Justice and Peace had lodged a complaint with the country's Election Commission alleging that Mr Modi's comments amounted to "blatant misuse of religion for political ends" and violated the election code of conduct.
After studying the complaints and "various inputs", the Election Commission said Mr Modi's remarks, at the first instance, appeared to violate the election code of conduct.
"The references to [Mr Sheikh] and linking his name to terrorism, made in the speech, amounts to indulging in activity which may aggravate existing differences, creating mutual hatred and causing tension between different communities," the Election Commission said in a letter to Mr Modi.
"[This] would involve violation... of the model code of conduct," the letter said.
Gujarat is going to elections next week
India's election code of conduct forbids any political party or candidate to "indulge in any activity" which creates religious tension, and prohibits places of worship to be used as "forum for election propaganda".
The Election Commission has asked Mr Modi to reply to the letter by Saturday afternoon.
Gujarat government lawyer KTS Tulsi has said he would resign if Mr Modi did not apologise for his remarks.
"Unless the chief minister gives a suitable clarification and offers to apologise, it is not possible to represent the Gujarat government as counsel," he said.
A BJP spokesman VK Malhotra has denied that Mr Modi has made any remarks which violated the code of conduct.
He said Mr Modi had only told the meeting that "if a terrorist is killed in an encounter [with the police] there was nothing wrong".
Gujarat goes to elections next week.
The Congress party has condemned Mr Modi's alleged remarks.
"The chief minister has virtually owned up to a murder and he has declared that he has a licence to kill," party spokesman Abhishek Singhvi has said.
Communist Party of India (Marxist) leader Sitaram Yechury has been quoted saying that Mr Modi's remarks were "shameful".
Gujarat government lawyer KTS Tulsi has said Mr Modi "will have to apologise for his remarks".
Mr Sheikh and his wife had been travelling by bus when they were taken away by the Gujarat police in November 2005.
At the time, police claimed Mr Sheikh belonged to the banned Kashmiri militant group, Lashkar-e-Toiba, and was plotting to assassinate Mr Modi.
Gujarat was rocked by religious riots in 2002
Gujarat has been heavily criticised for the treatment of its religious minorities.
According to official figures, more than 1,000 people, mostly Muslims, were killed during the riots that broke out after nearly 60 Hindus were killed when a train was set on fire in Godhra town, allegedly by a Muslim mob, five years ago.
The state administration was accused of not doing enough to stop the riots.
Security forces in India have on occasion admitted to extra-judicial killings - described by the local media as "fake encounters" - in which they had at first said they had killed militants after coming under gunfire.