The gunmen who opened fire outside Delhi's Jama Masjid on Sunday, injuring two foreigners, surveyed the area at least four times, police said on Monday after speaking to witnesses.
Doctors at Delhi's Lok Nayak Jai Prakash Hospital say the two Taiwanese tourists injured in the firing were now stable.
"Investigations are on," a Delhi police official said.
"We are taking the investigation forward based on eyewitness accounts. We have been told that the attackers recced the area at least four times," he said.
The police were hunting for people matching the account of the attackers, the official said.
The injured tourists, Ko Chang and Ku Ze Wei, both in their 20s, were shot in the head and stomach respectively when the gunmen fired at a bus from which a group of tourists was alighting outside gate 3 of the Jama Masjid around 11.30 am on Sunday.
There is speculation that the banned Indian Mujahideen group may be involved in the attack as it issued an e-mail threatening to derail the Commonwealth Games to avenge the killings of civilian protesters in the Kashmir Valley soon after the Jama Masjid shooting.
The attack came just two weeks before the Games starting Oct 3. A high alert was issued by the police Sunday and security has been tightened in the national capital.