Ukraine's President Volodymyr Zelensky has urged British MPs to designate Russia as a "terrorist state" after President Vladimir Putin ordered a special military operation against his nation and called for tougher sanctions on Moscow to "make sure our skies are safe".

The 44-year-old Ukrainian leader, who made a "historic" address to the House of Commons via videolink on Tuesday, received a standing ovation by members of Parliament.

"We are looking for your help, for the help of Western counties. We are thankful for this help and I am grateful to you, Boris," said Zelensky, addressing British Prime Minister Boris Johnson.

"Please increase the pressure of sanctions against this country (Russia) and please recognize this country as a terrorist state. Please make sure that our Ukrainian skies are safe. Please make sure that you do what needs to be done and what is stipulated by the greatness of your country. Glory to Ukraine and glory to the United Kingdom, he said.

While the West has imposed crippling sanctions on Russia, it has not yet cut off the supply of Russian oil to Western countries. Though Zelensky has sought a no-fly zone over Ukraine, the US and its allies seem unlikely to accept this to protect Ukrainians from Russian air power.

In an emotional address, Zelensky invoked Britain's war-time Prime Minister Winston Churchill's words, promising to fight Russian troops in the air, sea and on the streets.

"We will not give up and we will not lose, we will fight until the end, at sea, in the air... we will continue fighting for our land. Whatever the cost...we will fight in the forests, in the fields, on the shores, in the streets," he said.

In his address, Zelensky gave a day-by-day account of the attack by Russia, which began a fortnight ago.

He described how it was a war Ukraine "didn't start and we didn't want", but his country now had to fight.

"We do not want to lose what we have, what is ours... just the same way as you once didn't want to lose your country when the Nazis started to fight your country and you had to fight for Britain," he added.

And quoting Shakespeare, he said the question for Ukraine is "to be, or not to be... it's definitely yes, to be".

He concluded his speech by saying: "Do what you can, do what you must, because greatness obliges greatness, of your state and your people.

It marked the first time a foreign leader has directly addressed MPs in the Commons after Speaker Sir Lindsay Hoyle had confirmed his request.

Prime Minister Johnson said President Zelensky had "moved the hearts of everybody" watching, and pledged to "press on with tightening the economic vice" around Russian President Putin.

Labour leader Keir Starmer also praised "the bravery [and] the resolve" of the president and his people, adding: "He has shown his strength and we must show him - and the Ukrainian people - our commitment and support."

Zelensky's address followed Johnson's meetings with the leaders of Poland, Hungary, Slovakia and the Czech Republic to discuss the crisis in the region and the need to boost security efforts in central Europe.

Zelenskyy, a former comedian and actor turned politician, has been centre stage as Russian President Putin's forces began an armed conflict with Ukraine on February 24. Last week, he received a standing ovation when he spoke to the European Parliament, also via video link.

He has been in regular phone contact with Johnson, who launched a week of diplomacy to create a coalition against Russia's actions in Ukraine.

He hosted Canadian Prime Minister Justin Trudeau and Dutch Prime Minister Mark Rutte at Downing Street on Monday and later spoke with US President Joe Biden, French President Emmanuel Macron and German Chancellor Olaf Scholz to maintain pressure on Russia to isolate Putin diplomatically and economically.

It came as a plan to fast-track UK sanctions against allies of Vladimir Putin got through the House of Commons at rapid speed, backed by all parties on Monday. The UK government says its Economic Crime Bill will stop wealthy Russians from using the City of London for money laundering much quicker.

During the debate, condensed into a single day to try to get the measures into place as quickly as possible, UK Home Secretary Priti Patel said: "The UK must send a strong signal that it will not be a home for corruption."

The bill, which now goes to the House of Lords and is expected to become law later this month, contains several measures to tackle oligarchs and companies associated with Putin.

On February 24, Russian forces launched military operations in Ukraine, three days after Moscow recognised Ukraine's breakaway regions - Donetsk and Luhansk - as independent entities.