The U.S. and its allies and partners on the United Nations Security Council are circulating a draft resolution that would condemn Russia's invasion of Ukraine and impose "legally binding" obligations for Moscow to "immediately, unconditionally, and completely" withdraw its forces, a senior U.S. administration official said.

The U.S. fully expects Russia to veto the resolution during a vote Friday, but the official said the world must act to hold Russia accountable.

The U.S. mission, led by Ambassador Linda Thomas-Greenfield, is beginning "urgent diplomacy" now with every Security Council member to lobby support for this resolution, the official said, declining to comment on whether they think they can win support from veto-wielding China or partners like India and the United Arab Emirates who Thursday night did not condemn Russia.

While Russia may successfully block this resolution, the senior administration official said they would take action at the U.N. General Assembly, too, where Russia doesn't have a veto and all 193 members get a vote.

The official provided a brief preview of the resolution itself, saying it "would impose legally binding Chapter 7 obligations on Russia in response to its aggression against Ukraine" and "condemns in the strongest terms possible Russia's aggression, invasion, and violation of Ukraine's sovereignty. It reaffirms the sovereignty, independence, unity, and territorial integrity of Ukraine, and it requires the Russian Federation immediately, completely, and unconditionally to withdraw its forces."

It also calls for unhindered humanitarian assistance to those in need in Ukraine.

-ABC News' Conor Finnegan

On Thursday Ukrainians heard "not just rocket explosions, battles, the roar of aircraft," but the "sound of a new Iron Curtain lowering and closing Russia away from the civilized world," Ukrainian President Volodymyr Zelenskyy said in an address to the nation.

He said Ukraine has had "losses" and has captured Russian soldiers.

In eastern Ukraine's Donbas region, where Russian President Vladimir Putin announced he was recognizing the independence of two Russia-backed separatist areas, Ukraine's military is "doing great," Zelenskyy said.

Kharkiv in northeast Ukraine "is very difficult," he said, adding, "The most problematic situation today is in the south -- our troops are fighting fierce battles in the suburbs of [the southern city of] Kherson. The enemy is pushing out of the occupied Crimea, trying to advance towards Melitopol [a city in southeast Ukraine]."

"In the north of the country, the enemy is slowly advancing in the Chernihiv region, but there are forces to hold it," he said.

Zelenskyy said, "Ukraine did not choose the path of war -- but Ukraine offers to return to peace."

He said Ukrainians can help by joining the armed forces, saying,  "Any citizen with combat experience will now be useful. It is up to you and all of us whether the enemy will be able to advance further into the territory of our independent state."

Others can contributed by donating blood, he said, while politicians and community leaders should help "ensure normal life on the ground as much as possible."

-ABC News' Christine Theodorou

The leaders of the G-7 countries -- the U.S., the United Kingdom, Canada, France, Germany, Italy and Japan -- condemned Russia's attack in a joint statement, vowing to bring "severe and coordinated economic and financial sanctions."

The statement followed the leaders' Thursday morning meeting.

The group called on the Russians "to immediately de-escalate and to withdraw its forces from Ukraine," adding, "We also condemn the involvement of Belarus in this aggression against Ukraine and call on Belarus to abide by its international obligations."

The G-7 leaders asked the leaders of other nations to also come forwarding condemning the violence.

The leaders said they condemn Russian President Vladimir Putin recognizing the independence of two Russia-backed separatist areas in eastern Ukraine's Donbas region -- the self-proclaimed People’s Republics of Donetsk and Luhansk -- and urged "other states not to follow Russia’s illegal decision to recognise the proclaimed independence of these entities."

"We reaffirm our unwavering commitment to Ukraine’s sovereignty and territorial integrity within its internationally recognised borders and territorial waters as well as the right of any sovereign state to determine its own future and security arrangements," the G-7 leaders said.

They continued: "We condemn President Putin for his consistent refusal to engage in a diplomatic process to address questions pertaining to European security, despite our repeated offers. We stand united with partners, including NATO, the EU and their member states as well as Ukraine and remain determined to do what is necessary to preserve the integrity of the rules-based international order. In this regard, we are also closely monitoring global oil and gas market conditions, including in the context of Russia’s further military aggression against Ukraine. We support consistent and constructive engagement and coordination among major energy producers and consumers toward our collective interest in the stability of global energy supplies, and stand ready to act as needed to address potential disruptions."

An overnight curfew will be imposed in Kyiv, Mayor Vitali Klitschko said. Residents must stay home between 10 p.m. and 7 a.m., with only workers involved in critical infrastructure and services allowed out.

Kyiv’s metro is also now being used as a bomb shelter.

-ABC News' Patrick Reevell