Before Russia's invasion, there were around 20,000 Indians in Ukraine. About 8,000 have since managed to leave the country, of whom some 1,400 have been flown back to India, according to officials.
According to Indian media, some students are facing difficulties crossing into neighbouring countries, with some Ukrainian border guards reportedly refusing to let them pass and demanding money.
"I was standing near the Ukrainian border, awaiting my turn to enter Romania when I saw a few guards point guns at Indian students and start abusing them in their language," the Times of India quoted one student as saying.
"Students, who were already scared, started screaming in terror."
The Hindustan Times quoted Ishika Sarkar, a student in eastern Ukraine, saying in a video that Indians in the area were in bunkers and running short of food.
"(We) have been asked to reach the western border, which is impossible for us because the connecting bridges have been blown up due to bombardment ... but we are not getting any kind of help in Ukraine," he said.
Aruj Raj, a student in Kharkiv, told the paper that he has been in a hostel bunker with 400 other Indian students since last Thursday.
"There is so much bombing happening outside. We can see street fighting through our windows. The city is still under curfew. It is impossible for us to step outside. We hardly have anything left to eat or drink," he said.
India, which has long walked a tightrope in its relations with Moscow and the West and which gets most of its arms from Russia, last week abstained in the United Nations Security Council resolution deploring Russia's "aggression".