"The main challenges in evacuation of Indians from Sumy are ongoing shelling, violence and the lack of transportation," said foreign ministry spokesperson Arindam Bagchi.
"We are exploring multiple options to evacuate Indian citizens from there," he added, saying India is pressing both the countries for a ceasefire to provide a safe passage out for the civilians.
Almost all the Indians stranded have left Ukraine's Kharkiv and they will be evacuated in the next few hours, said the government, adding, the "main focus" is on conflict-stricken Sumy now.
"From Pisochyn and Kharkiv, we should be able to clear out everyone in the next few hours, so far I know almost all Indians have left Kharkiv. The main focus is on Sumy now," it said.
Three buses have reached Pisochyn and will shortly be making their way to western Ukraine, carrying the stranded students from the area, which is around 11 km from Kharkiv, said the foreign ministry in a press briefing.
Hundreds of students are stuck in eastern Ukrainian city Sumy, one of the conflict zones witnessing intense fighting between Russian and Ukrainian forces.
Earlier in the day, the stranded students in Sumy city shared videos saying they have decided to take a risky journey to the Russian border that's 50 kilometres away. They, however, decided to stay put after the government contacted them and advised to "avoid unnecessary risks".
Around 13,300 people have returned to India so far and 13 flights are scheduled for the next 24 hours, said the government. He said a total of 15 flights have landed in the last 24 hours with around 2,900 onboard.
Russia's invasion of Ukraine on February 24, has sent nearly 1.5 million refugees fleeing westward into the European Union and provoked unprecedented international sanctions on Moscow and warnings of a global recession.