He stressed that an evacuation mission from Mariupol continues with the mediation of the United Nations and the International Committee of Red Cross.
Zelensky said more than 40 civilians, including women and children, were evacuated from Azovstal on May 6.
The Ukrainian president also said that Ukraine was working on diplomatic options to save the soldiers who still remains at Azovstal.
"Influential mediators are involved. Influential states," he said.
Earlier, Deputy Prime Minister of Ukraine Iryna Vereshchuk said that that 50 children, women and elderly people were evacuated from Azovstal on May 6.
The Ukrainian authorities said they were planning to continue the evacuation on the morning of May 7.
On May 6, Russian troops in Mariupol fired at a car that was evacuating civilians from Azovstal. One soldier was killed and six more were injured as a result of the attack.
On May 4, a total of 344 people were evacuated from Mariupol, Manhush, Berdyansk, Tokmak, and Vasylivka, and reached Zaporizhzhya. On May 3, more than 100 Mariupol residents from Azovstal had finally arrived in the city.
On May 2, the Deputy Commander of the Azov Regiment, Captain Svyatoslav Palamar, said that up to 200 civilians were still trapped at Azovstal, which was constantly being stormed and shelled by the Russian invaders.
On May 1, President Zelensky said that the evacuation of civilians from Azovstal was underway. The effort is being conducted by the UN and the International Committee of Red Cross. Prior to that, the Russian side disrupted the evacuation or forcibly deported Mariupol residents to the occupied territories and the Russian Federation.