After a first round of talks with Russia, Ukrainian President Volodymyr Zelenskyy says his country received what he described as signals from the Russian side.

Zelenskyy on Monday used Facebook to comment on the talks after the two sides agreed to continue dialogue.

Zelenskyy admitted the negotiations were difficult. But he said his delegation had received certain signals from the Russian side, adding that these would be analyzed as a means of deciding how to proceed in the second round of talks.

In the first round, neither side is thought to have given ground. Ukraine is calling for an immediate ceasefire and withdrawal by Russian troops, while Moscow demands demilitarization and neutrality for Ukraine.

It remains unclear whether there will be sufficient movement in the second round of negotiations, expected in a few days' time, to bring a cessation to the Russian onslaught.

Russian forces continue their offensive despite the talks. They are aiming at Ukraine's capital, Kyiv, and the second largest city of Kharkiv. Local media report that they are also laying siege to the southern city of Kherson.

Zelenskyy signed an application for his country's membership in the European Union on Monday, in a move thought to be aimed at bolstering his country's position in the face of Russian aggression.