Around 300 Indians are stuck in Kharkiv and 700 are in Sumy, the MEA said.
At least 1,000 Indians - 700 in Sumy and 300 in Kharkiv - are still stranded in conflict zones in eastern Ukraine, the government said on Friday, adding that arranging buses to evacuate them was proving to be the biggest challenge right now.
"We will continue Operation Ganga till the last person gets evacuated. Roughly 2,000-3,000 (more Indians) are likely to be there (in Ukraine), the number can vary," Ministry of External Affairs Spokesperson Arindam Bagchi said at a briefing.
"Our primary focus is to get Indian students out of conflict zones in eastern Ukraine. We are urging both sides (Russia and Ukraine) to find ways so that we can take out our citizens. A local ceasefire would help," he added.
Indian medical students stranded at the Sumy State University issued a desperate plea for help earlier in the day, saying they were 800-900 were trapped in their hostels without much food or water while there was gunfire, shelling and freezing temperature outside.
"We have been expecting the government to help, but we have got no information. Some are saying buses are waiting at the Russian border, which is about 50 km from here. If we walk from the hostel, there are snipers in all four directions, everywhere. We fear airstrikes. Bombardment is happening every 20 minutes," they said in a video.
"We request Narendra Modi ji, please take us out of here, or else we will be killed. If we walk out from here on our own, we will be killed. We request the government of India, please help us," they said.
"There is no food, no water. No water in the toilets. Many haven't had water to drink since last night. We are very worried," they added.
The Indian embassy last week warned of intense fighting in Kharkiv, Sumy and Kyiv. Reports say trains and buses have stopped running in Sumy, roads and bridges out of the city have been destroyed, and there is heavy street fighting.
Mr Bagchi said around 20,000 Indians have left Ukraine's borders since India issued its first travel advisories in mid-February.
He said 15 flights landed in India as part of the evacuation mission during the last 24 hours, bringing back more than 3,000 nationals.
The spokesperson said 16 flights are scheduled for the next 24 hours.
Over 10,300 Indians brought back in 48 flights under 'Operation Ganga' so far, he added.