Anuj Bidve, 23, was murdered in the early hours as he walked with friends from his hotel in Salford, an area to the west of Manchester, towards the city centre.
Greater Manchester Police (GMP) called it an "awful" and "unprovoked" attack and vowed their investigation would "leave no stone unturned".
"This is a tragic incident and our first thoughts are for the family," said chief superintendent Kevin Mulligan.
"There is going to be a huge amount of concern in the community and I can reassure the family and the community by telling them we have launched a major investigation and no stone will be left unturned until we find the people who are responsible for this."
When asked if the murder could have a racial motivation, Mulligan said: "We are investigating every possible aspect."
Bidve, who was studying a micro-electronics postgraduate qualification at Lancaster University, around 40 miles from Manchester, was enjoying a short break in the city with eight friends.
The group was stopped by a man who spoke to them before shooting Bidve at close range.
Mulligan urged the killer, described as a white man in his 20s, to surrender himself to the police as soon as possible.
Bidve's family in India has been informed.
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We are all praying for his soul to rest in peace
what are we supposed to do?
He was my friend in Lancaster..... we are all in state of shock...... Please pray God forgives him and may his soul rest in peace... Aameen !