Home Minister Sushilkumar Shinde said he had asked the NIA to probe the case. Jammu and Kashmir Chief Minister Omar Abdullah had earlier asked for an NIA probe into the issue.
Shah, a resident of Dardpora village in Kashmir's Kupwara district, was arrested from Uttar Pradesh's Gorakhpur March 20 when he entered India through the Sunauli checkpost on the India-Nepal border. He had flown to Kathmandu from Karachi.
There are two conflicting versions on Shah's arrest. While Delhi Police claim he was part of a terrorist plot attempting to launch a fidayeen (suicide) attack in the capital, Jammu and Kashmir Police say he was on his way back home from Pakistan to surrender under the rehabilitation policy of the government.
Officials said the NIA has been asked to examine the versions of the two police forces and give its view.
Abdullah had Saturday discussed Shah's arrest with Shinde and had emphasised that the case should be probed by the NIA to establish the facts.
Shah's family has also claimed he was returning home in the Kashmir Valley under the rehabilitation policy for surrendered militants.
Sources said Jammu and Kashmir government had sought to produce evidence to back its claim about Liyaqat being a former militant on his way back home under the state's surrender-cum-rehabilitation policy.
They said a list had been handed over to the home ministry which comprised names of people who had crossed over to Pakistan-administered Kashmir and now wanted to surrender by traveling via Nepal.
Delhi Police chief Neeraj Kumar met home ministry officials Monday. Delhi Police has said that information about arrival of Liyaqat had been based on its intelligence. It had Sunday released the sketch of a man who was "contact" of Liyaqat in the supposed terror plan.
The police said the man, aged around 25-30, had brought the arms and explosives, to be used in the attack, to a guest house here.