“We note that with the co-operation of the Ukrainian authorities, many students have left Kharkiv yesterday,” Indian foreign ministry spokesperson Arindam Bagchi said in a statement.
“We have not received any reports of any hostage situation regarding any student.”
Ukraine has also denied holding back Indian citizens.
Prime Minister Narendra Modi and Russian President Vladimir Putin spoke by telephone late on Wednesday to discuss the safe evacuation of Indian students from Ukraine.
Russia's embassy in India said they were trying to organise an urgent evacuation of a group of Indian students from Kharkiv through a “humanitarian corridor” to Russia, from where they would be flown back to India.
“These students are actually taken hostage by the Ukrainian security forces, who use them as a human shield and in every possible way prevent them from leaving for Russia,” the Russian embassy said.
Before the conflict began, Indians made up about a quarter of the 76,000 foreign students in Ukraine, the largest group, according to Ukrainian government data.
India has declined to condemn the invasion by its old friend Russia, though it has called for an end to the violence.