Speaking publicly about his visit to Ukraine for the first time since returning home, U.S. Secretary of State Antony Blinken declared to the Senate Foreign Relations Committee that “the Ukrainians have won the battle for Kyiv.”

Blinken, who visited Ukraine over the weekend with U.S. Defense Secretary Lloyd Austin, emphasized the need for additional aid to help Ukrainians weather the ongoing war as it enters its next phase.

“As we took the train across the border and rode westward into Ukraine, we saw mile after mile of Ukrainian countryside, territory that just a couple of months ago, the Russian government thought that it could seize in a matter of weeks. Today -- firmly Ukraine's," Blinken told the committee.

Blinken said that while in Kyiv, he saw the signs of "a vibrant city coming back to life" with people eating outside, sitting on benches and strolling the streets.

“For all the suffering that they've endured, for all the carnage that Russia's brutal invasion continues to inflict, Ukraine was and will continue to be a free and independent country," he said.

Blinken said the United States has played a vital part in helping Ukrainian forces mount an effective resistance against Russia.

“I have to tell you, I felt some pride in what the United States has done to support the Ukrainian government and its people and an even firmer conviction that we must not let up," Blinken said. "Moscow's war of aggression against Ukraine has underscored the power and purpose of American diplomacy."

He added, "We have to continue to drive that diplomacy forward to seize what I believe are strategic opportunities, as well as address risks presented by Russia's overreach as countries are reconsidering their policies, their priorities, their relationships."

-ABC News' Shannon Crawford and Conor Finnegan

Prior to meeting Russian President Vladimir Putin on Tuesday, U.N. Secretary-General Antonio Guterres issued a statement calling for humanitarian corridors in Ukraine that are "truly safe."

Guterres later raised the issue with Putin during a face-to-face meeting, stressing the urgent need for the creation of safe and effective humanitarian corridors in the war-ravaged Ukrainian port city of Mariupol, where he said thousands of civilians remain trapped, according to the Russian state-run TASS news service. Guterres also proposed the creation of a humanitarian contact group.

"We urgently need humanitarian corridors that are truly safe and effective, and that are respected by all to evacuate civilians and deliver much needed assistance," Guterres said prior to meeting with Putin. "To that end, I have proposed the establishment of a humanitarian contact group, bringing together the Russian Federation, Ukraine, and the U.N. to look for opportunities for the opening of safe corridors, with local cessation of hostilities and to guarantee they are actually effective."

Guterres made his statement following a meeting with Russian Foreign Minister Sergey Lavrov.

While meeting with Guterres, Putin said the U.N. chief has been misled and insisted that humanitarian corridors in Mariupol are functioning, according to TASS.

"You say that Russia's humanitarian corridors are not operating. Mr. Secretary-General, you have been misled: these corridors are operating," Putin said, according to TASS.

Putin told Guterres that up to 140,000 people had fled Mariupol with the assistance of Russia.

"And they can go anywhere. Some want to go to Russia; some want to go to Ukraine. Anywhere! We do not keep them, we provide all kinds of help and support," Putin said, according to TASS.

However, Putin “agreed, in principle, to the involvement of the United Nations and the International Committee for the Red Cross in the evacuation of civilians from the Azovstal plant in Mariupol," according to a readout of the meeting provided by the U.N.

The U.N. General Assembly -- where all 193 countries have a vote -- has unanimously adopted a resolution that creates a new accountability mechanism.

Now, whenever a permanent member of the U.N. Security Council uses its veto power to block a resolution, it will automatically trigger a debate in the General Assembly within 10 days.

The move was made primarily in response to Russia's veto power, which the country has used repeatedly to sink resolutions about its own aggression. It has paralyzed the ability of the Security Council, the United Nation's most powerful body, to check Russia.

The United States, Russia, China, France and the United Kingdom are the five veto-wielding permanent members of the Security Council, while the ten other seats rotate and are won by election.

The United States and Liechtenstein co-sponsored the resolution, with the tiny European country tweeting, "Together we have made sure today that a veto is no longer the last word on issues of peace and security."

-ABC News' Conor Finnegan

U.S. Defense Secretary Lloyd Austin said Tuesday that any public statements by world leaders that the conflict in Ukraine could spin out of control and lead to a nuclear confrontation is "unhelpful and dangerous."

Austin's comments during a news conference at Ramstein Air Base in Germany came a day after Russian Foreign Minister Sergei Lavrov warned of a "serious" risk of nuclear war over Ukraine.

"The danger is serious, real. It can’t be underestimated,” Lavrov said in a Russian state TV interview late Monday.

Lavrov said that following the Cuban missile crisis of 1962, the United States and the former Soviet Union developed an understanding of the rules of conduct between the two superpowers and have avoided a nuclear confrontation for 60 years. "Now there are few rules left," Lavrov said.

Austin was asked during Tuesday's news conference whether the conflict in Ukraine could spin out of control and lead to a nuclear confrontation.

"We certainly will do everything within our power and Ukraine will have the same approach, do everything within their power to make sure it doesn't spin out of control. The international community is focused on that as well," Austin said. "There's always a possibility that a number of things can happen. But, you know, again, I think it's unhelpful and dangerous to rattle sabers and speculate about the use of nuclear weapons."

-ABC News' Matt Seyler

Mariupol has not yet fallen, despite Russia's demands that Ukrainian troops defending the besieged Ukrainian port city surrender, according to Ukrainian Prime Minister Denys Shmyhal.

"There [are] still our military forces, our soldiers, so they will fight until the end," Shmyhal told ABC News' George Stephanopoulos in an exclusive interview Sunday on "This Week."

Mariupol is a strategic city for Moscow because it would allow Russian forces in the south to connect with troops in eastern Ukraine's contested Donbas region. It would also give Moscow a key port.

Although Mariupol remains under the Ukrainian government's control, Shmyhal said the city's residents are suffering.

"They have no water, no food, no heat, no electricity," he said. "They ask all of our partners to support and help stop this humanitarian catastrophe."

-ABC News' Monica Dunn