India's supreme court has sought clarification 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, commented on the 2005 killing of a man by police in Gujarat.
Media reports suggested that Mr Modi had "justified" the killing of Sohrabuddin Sheikh, a Muslim civilian.
Mr Modi denied the allegation and told election authorities that he had been misquoted by the media.
In March, the Gujarat police admitted - at a hearing of the Supreme Court - that Sohrabuddin Sheikh, a Muslim civilian, was killed in a staged gun-battle.
Next month, three top policemen in the state were charged with the murder of Mr Sheikh.
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.
Gujarat is in the middle of state elections where Mr Modi's party is contesting the Congress party.
The supreme court has asked Mr Modi to reply by end of January.
'Contempt of court'
It rejected his contention that the remarks on Mr Sheikh were "political", and he was reacting to election speeches made by the opposition.
Gujarat is in the middle of state elections
A lawyer appearing for Mr Sheikh's brother, Dushyant Dave, was quoted in The Hindu newspaper as saying in the court that Mr Modi's statement was a "gross contempt" of court and "affront to humanity and the Supreme Court".
"If this court were to show leniency in this case, it will embolden politicians to say whatever they want and go scot free," he told the court.
A lawyer appearing for Mr Modi's government, Mukul Rohatgi, denied this and said Mr Modi's remarks were political.
"Election speeches are often exaggerated and contain hyperboles," Mr Rohatgi reportedly told the court.
Earlier a human rights group 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.
Mr Modi denied the allegation and said he was misquoted by the media.
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".
Gujarat was rocked by religious riots in 2002
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 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.