More than 13,000 people have been killed in the conflict in eastern Ukraine, which began in 2014 after a pro-Western revolution in Kyiv and Moscow's annexation of Crimea.

"In recent weeks, we have seen a very dangerous tendency to increase the number of ceasefire violations by the Russian occupation forces and the number of Ukrainian defenders killed," Zelenskyy said in a statement.

On Tuesday, two more military soldiers were shot dead in fighting with pro-Russian separatists in eastern Ukraine, the country's army said.

Ukraine's army has accused the separatists of firing on Ukrainian positions with machine guns and grenade launchers.

The first incident took place near the town of Avdiivka in the Donetsk region, the second near the town of Zolote-4 in the Lugansk region, the press service of the Ukrainian military operation told AFP. Both soldiers died from their wounds on Monday, the authorities said.

The deaths come amid rising tensions and clashes along the frontline, raising fears of an escalation of the conflict.

Zelenskyy also called on NATO member countries to strengthen their military presence in the Black Sea region.

"Such a permanent presence should be a powerful deterrent to Russia, which continues the large-scale militarisation of the region and hinders trade shipping," said Zelenskyy.

"We are committed to reforming our army and defence sector, but reforms alone cannot stop Russia," Zelenskyy said.

"NATO is the only way to end the war in Donbas. The MAP (membership action plan for joining NATO) will be a real signal for Russia."

Responding to Zelenskyy's NATO comments, Dmitry Peskov, spokesman for the Russian presidency, told reporters: "We strongly doubt that this can help Ukraine to solve its internal problem. From our point of view, it will make the situation even worse."

Ukraine has accused Russia of building up its forces near Ukraine’s eastern borders in recent weeks, as well as in the Crimean peninsula annexed by Moscow in 2014.

Russia claims that its troop movements on their own are not threatening and says Kyiv is responsible for the clashes on the front line.

However, the United States, the United Kingdom, and NATO countries have all expressed their support for Ukraine.

On Monday, the European Union's chief diplomat Josep Borell said he was following the Russian military activity near Ukraine with "severe concern".

"Unwavering EU support for Ukraine's sovereignty and territorial integrity," he added on Twitter.

Ukrainian forces also said they have launched ten days of exercises in the south of the country to protect "the administrative border with Crimea" and "parts of the coastline accessible by landing".

Ukraine's President has also stressed that the conflict is the country's most urgent issue in their hope of joining NATO

EU very worried over Russian military activity near Ukraine's border

The European Union has expressed "great concern" over the movement of Russian military forces near the border with Ukraine.

Josep Borrell, the bloc's foreign affairs chief, also expressed "unwavering support" for Kyiv after a phone conversation with Ukraine's foreign minister Dmytro Kuleba.

"We are following with severe concern the Russian military activity surrounding Ukraine," Borrell tweeted on Sunday.

"Unwavering EU support for Ukraine's sovereignty and territorial integrity," he added

Borrell said he would hold talks with Kuleba and the EU's 27 foreign ministers at an upcoming meeting in April. Other western leaders, including incoming US President Joe Biden, have said they stand by Ukraine.

Kyiv has accused Russia of massing troops on its northern and eastern borders and in the Crimean peninsula annexed by Moscow in 2014.

The Kremlin did not deny the recent military movements but insisted it was "not threatening" anyone.