The chief minister said there was no question of asking Navjot Singh Sidhu, the Tourism, Culture and Local Government minister, to quit.
Last week, the state government in the Supreme Court had favoured the Punjab and Haryana High Court verdict convicting and awarding a three-year jail term to Mr Sidhu in the 1988 case.
Amarinder Singh pointed out that the Supreme Court had stayed Sidhu's conviction in 2007 and was yet to pronounce its final verdict on his petition challenging the high court order.
Mr Sidhu had allegedly hit a 65-year-old man, Gurnam Singh, on the head during an argument on a road in Patiala on December 27, 1988. Gurnam Singh died of a haemorrhage in the hospital.
The question of the minister resigning, merely because the state government had repeated its stand of 30-years in the case before the Supreme Court, did not arise, he added.
"There was neither any impediment in Sidhu's induction into the cabinet nor in his continuation now, in view of the stay on his conviction", Mr Amarinder said in a statement here.
The categorical clarification from the chief minister came amid reports suggesting that Mr Sidhu had been asked to resign, and also in the wake of the demand from the opposition that he should step down.
Reacting to reports suggesting that the government had deliberately not supported the minister in the Supreme Court, the chief minister stressed that unless the prosecution received new inputs, it was not legally possible for it to add a new element to its arguments.
"Taking a U-turn from the stand taken by the government in the trial and high courts was not an option for the government," he added.
In September 1999, a trial court had acquitted Mr Sidhu of the murder charge. However, the High Court reversed the verdict and held him and co-accused Rupinder Singh Sandhu guilty of culpable homicide not amounting to murder in December, 2006.
The high court sentenced them to three-year imprisonment and imposed a fine of Rs 1 lakh each on the convicts.
After the Punjab government favoured a court verdict convicting Mr Sidhu in the road rage case, the minister had tried to put on a brave face, saying he was ready to carry "any burden" that he may have to because of his own government's stance, even as Opposition demanded he quit the cabinet.