Shafaq News/ Ukrainian President Volodymyr Zelenskiy on Monday asked the European Union to allow Ukraine to gain membership under a special procedure immediately as it defends itself from invasion by Russian forces.

"Our goal is to be with all Europeans and, most importantly, to be equal. I'm sure that's fair. I am sure we deserve it," he said in a video speech shared on social media.

Prove that you are with us," Zelenskiy told the European Union on Tuesday, a day after Kyiv officially asked to join the bloc as it battles invading Russian forces.

EU lawmakers, many wearing #standwithUkraine T-shirts bearing the Ukrainian flag, others with blue-and-yellow scarves or ribbons, gave Zelenskiy a standing ovation as he addressed the European Parliament via video link.

"We are fighting to be equal members of Europe," Zelenskiy said in Ukrainian in a speech translated into English by an interpreter who spoke through tears.

"Do prove that you are with us. Do prove that you will not let us go. Do prove that you are indeed Europeans, and then life will win over death and light will win over darkness," he said. "The EU will be much stronger with us."

Zelenskiy has remained in Kyiv to rally his people against the invasion. As he spoke to EU lawmakers and top officials, a Russian armoured column was bearing down on Ukraine's capital.

"We are (with you)," European Commission vice-president Maros Sefcovic said in response to Zelenskiy's appeal, saying the EU would provide Ukraine with weapons, on top of slapping unprecedented sanctions on Russia after it invaded Ukraine last week.

The presidents of eight central and eastern European nations on Monday published an open letter calling for Ukraine to be granted immediate EU candidate status and for the start of formal membership talks.

Ukraine is well aware, however, that any membership process will be long and difficult, even if it manages after the war to avoid falling back under Moscow's domination.

Charles Michel, the chairman of EU leaders, told the EU Parliament after Zelenskiy's speech that the bloc would have to seriously look at Ukraine's "legitimate" request to join.

But he added: "It is going to be difficult, we know there are different views in Europe (about further enlargements)."

The European Parliament adopted a non-binding resolution - by 637 votes to 13, with 26 abstentions - calling for tougher sanctions "aimed at strategically weakening the Russian economy and industrial base, in particular the military-industrial complex".

While Russian President Vladimir Putin "recalls the most dreadful statements of 20th century dictators", Zelenskiy is being "heroic", they said.

The European Parliament also urged EU leaders to be tougher on oligarchs and officials close to Putin, restrict oil and gas imports from Russia, ban Russia and its ally Belarus entirely from the SWIFT bank messaging system, and to close all EU ports to Russian ships or ships headed to or from Russia.

However, EU lawmakers rejected an amendment calling Russia a "rogue state".

Russia calls its actions in Ukraine a "special military operation" aimed at ridding the country of leaders it characterises as "neo-Nazis and drug addicts".

European Commission president Ursula von der Leyen said Putin's decision to invade Ukraine had had the effect of uniting countries against Russia.

"If Putin was seeking to divide the European Union, to weaken NATO, and to break the international community, he has achieved exactly the opposite," von der Leyen told the EU Parliament, a blue and yellow ribbon pinned to her jacket.