The second attempt to evacuate civilians from the easternern port city of Mariupol failed on Sunday as fighting broke out, according to the International Committee of the Red Cross.
The evacuation of civilians remains a big concern, especially from areas of Ukraine where Russian forces have been pounding.
For India, the focus is on Sumy where some 700 Indian students are stranded whose fate is not known.
India announced the start of the last leg of its operation to evacuate Indian students stranded in Ukraine, as the conflict entered its 11th day on Sunday. More than 13,300 students were brought back on 63 flights on Saturday.
India has called on both Russia and Ukraine to observe a ceasefire so that students can be safely evacuated. However, the fighting has continued and a truce is yet to materialise.
The Indian embassy in Ukraine has asked all Indians still in the country to fill up an online form along with details of their current location.
“All Indian nationals who still remain in Ukraine are requested to fill up the details contained in the attached Google Form on an URGENT BASIS. Be Safe Be Strong,” the embassy said in a tweet.
The locations mentioned in the form included Cherkassy, Chernihiv, Chernivtsi, Dnipropetrovsk, Donetsk, Ivano-Frankivsk, Kharkiv, Kherson, Kyiv, Luhansk and Lviv.
The Indian embassy in Hungary has asked all Indians staying on their own in that country to assemble at the Hungary City Centre in capital Budapest for evacuation.
Meanwhile, Russian President Vladimir Putin in a telephone call with his French counterpart Emmanuel Macron blamed Kyiv for failed civilian evacuations from Mariupol.
The wait, however, has got longer as fierce fighting blocks their way to safety across the Russian border.
They have abandoned the idea of undertaking an arduous journey to the Russian border on foot amid fusillades of artillery fire and missile barrages, a day after the Indian government assured them they will be evacuated safely.
The Indian embassy in Hungary suggested that the evacuation mission from the country is nearing completion as it is beginning the last leg of flights under the operation.
India has been bringing back its nationals from Romania, Poland, Hungary, Slovakia and Moldova after they crossed over to these countries from Ukraine through land border transit points.
The first flight had returned with the stranded Indians on February 26 from Bucharest.
According to the officials, around 2,500 Indians were evacuated on 13 flights in the last 24 hours.
They said seven flights are scheduled over the next 24 hours to bring back stranded Indians from Hungary, Romania and Poland.
"Under Operation Ganga, so far 76 flights have brought over 15,920 Indians back to India.
Out these, 13 flights landed in the last 24 hours," said an official.
Prime Minister Narendra Modi, who was in Pune, attributed the success of 'Operation Ganga' to India's growing influence in the global arena.
We are evacuating thousands of Indians safely from the war zone through the Operation Ganga, Modi said after inaugurating the golden jubilee celebration of the Symbiosis University and its Arogyam Dham.
It is due to India's growing influence that it has brought thousands of students from the war zone of Ukraine back to their motherland, he said, adding many big countries are facing difficulties in doing so for their citizens.
The Indian embasy in Hungary posted an "important announcement" on Twitter asking Indian students who are still in that country to report to designated contact points for return to India.
"Important Announcement: Embassy of India begins its last leg of Operation Ganga flights today.
All those students staying in their OWN accommodation ( other than arranged by Embassy) are requested to reach @Hungariacitycentre, Rakoczi Ut 90, Budapest between 10 am-12 pm," it said.
Officials said over 21,000 Indians came out of Ukraine since the issuance of an advisory weeks before the conflict began.
Out of these, 19,920 have already reached India, they said.
Indian student Harjot Singh, who was shot multiple times while trying to flee the Ukranian capital Kyiv a few days back, is returning to Delhi on Monday, Minister of State for Civil Aviation V K Singh said.
"Harjot Singh is the Indian who was shot during the war in Kyiv.
His passport was also lost in the chaos," VK Singh, who was dispatched to Poland to coordinate the evacuation efforts from there, tweeted, adding the student is reaching India with him on Monday.
On March 1, medical student Naveen SG from Karnataka was killed in shelling in the Ukrainian city of Kharkiv when he ventured out to buy food for himself and fellow students.
The Ukrainian airspace has been shut since February 24 due to the Russian military offensive.
Indian citizens stuck in Ukraine were being airlifted once they crossed over to neighbouring countries such as Romania, Hungary, Slovakia and Poland.
However, evacuating those stranded in Sumy on the eastern side poses a formidable challenge because of the ceaseless bombing and shelling by the Russians.
Exasperated over the delay in their evacuation, the students in Sumy had on Saturday posted a video clip declaring they had decided to risk the walk to the Russian border in biting cold amid the fighting, raising fears about their safety in the corridors of power in New Delhi.
25-year-old Jisna Jiji, a medical student, said they have no option but to wait patiently as walking to the Russian border is fraught with danger.
Soon after the video went viral, the Indian government asked the students to remain in shelters and assured them they will be rescued soon.
Aashiq Hussain Sarkar, also a medical student, tweeted, "Every day at 6 AM students are waiting for buses on the road. We still believe today is the day. But they keep postponing the date everyday. So please Don't break our Hopes. #Sumy".
Jiji said many students were crammed in the basements of their hostels, melting snow to quench their thirst with little food left and power and water lines snapped.
"We are still in Sumy. We have not got any update yet when will we be evacuated. But we cannot continue like this for longer. Our problems are increasing day by day. We appeal to the government to update us immediately," said a girl in a video message.
"There is no water here, electricity supply has been disrupted. There's no money in ATMs, girls don't have sanitary napkins," said another despairing student in the same video.
India had on Saturday "strongly pressed" the Russian and Ukrainian governments through multiple channels for an immediate ceasefire in Sumy to ensure a safe passage for around 700 Indian students stuck there, but with no success so far, while the war entered its 10th day on Sunday.
(With PTI Updates)