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2 year oldVolodymyr Zelensky said via video link that Ukraine was enduring a 9/11 every day as it battled Russian forces.
He again urged the US and Nato allies to enforce a no-fly zone over Ukraine, saying: "I need to protect the sky."
US President Joe Biden is later set to sign off an extra $800m (£612m) in military aid to Ukraine.
Mr Zelensky urged the assembled US politicians to remember coming under attack in the past - at Pearl Harbor in 1941 and on 11 September 2001 - saying Ukrainians were experiencing the same thing every day.
"In your great history, you have pages that would allow you to understand the Ukrainian history. Understand us now," he said.
He also referenced US civil rights leader Martin Luther King's famous speech: "I have a dream, these words are known to each of you - today I can say I have a need. I need to protect the sky," he said.
The Ukrainian leader also showed a video of missile strikes on his country's cities and the resulting dead and wounded people.
He has repeatedly called on Nato to impose a no-fly zone over his country's airspace, but Nato has refused.
A no-fly zone over Ukraine would mean that Nato forces would have to engage directly with any Russian planes spotted in those skies and shoot at them if necessary.
As an alternative to a no-fly zone, Mr Zelensky pleaded for air-defence systems and aircraft.
He has previously asked the US and the EU for Polish MiG-29 fighter jets, but this has been rejected by Mr Biden over fears this would pull Nato members into the war.
Addressing President Biden directly in English, President Zelensky said: "I wish you to be the leader of the world. Being the leader of the world means being the leader of peace."
Volodymyr Zelensky again demonstrated he had a firm grasp on how to plead his nation's case to a foreign audience in a language they could understand - both literally and figuratively.
Speaking to the British Parliament last week, the Ukrainian president referenced Winston Churchill. In his video address to Congress on Wednesday, Zelensky compared his nation's daily aerial bombardment to Pearl Harbor and September 11.
He also mentioned the carvings of US presidents at Mount Rushmore and Martin Luther King Jr's I Have a Dream speech - saying his nation had a "need" for more US assistance.
The American public has been transfixed by video footage of the Russian onslaught, and Zelensky used sometimes graphic images of dead and injured children and bombed cities to drive home his request to "close the skies" to Russian attacks.
Then the former actor made one final gesture of theatrical flair, ending his speech in English, framing the fight in Ukraine as a battle for the values of Europe and the world.
When the stakes are framed this way, Zelensky may hope, it will be difficult for the US and its allies to say no.
After the speech, House Speaker Nancy Pelosi tweeted that it had been a "distinct privilege" to hear from the Ukrainian president, and that the US was "unwavering in our commitment to the people of Ukraine as they courageously defend democracy".
The $800m in funding set to be signed off later will go towards anti-armour and anti-aircraft weapons, such as Stingers and Javelins, US media report.
The funding is covered by a spending bill on humanitarian, defensive and economic assistance to Ukraine that was approved by Congress last week.
In the past year, the Biden administration has provided $1.2bn in weapons for the country, including Mi-17 helicopters, patrol boats and small arms such as grenade launchers and machine guns, the New York Times reports.
On Wednesday, attacks by Russian forces continued in cities and towns across the country:
Meanwhile, Nato defence ministers are meeting in Brussels to discuss their response to the invasion.
Mr Biden is expected to travel to Brussels next week to meet Nato allies and participate in a summit of European Union leaders.
The US president will "discuss ongoing deterrence and defence efforts," and reaffirm his country's commitment to its Nato allies, White House press secretary Jen Psaki has said.
On Tuesday, the prime ministers of Poland, Slovenia and the Czech Republic met Mr Zelensky in the evening as a curfew began in the Ukrainian capital, Kyiv.
Afterwards, the Czech leader told Ukrainians that they were "not alone". The group are the first Western leaders to visit Ukraine since Russia invaded last month.