GEOFF BENNETT: The International Criminal Court's decision to issue an arrest warrant for Russian President Vladimir Putin today marks the first time in history that the ICC has indicted a head of state from a permanent member of the U.N. Security Council.

It's the most dramatic step taken to try and hold Russia accountable for the war in Ukraine.

Nick Schifrin starts our coverage.

NICK SCHIFRIN: Of all Russian crimes committed in Ukraine, mass graves, cities reduced to rubble, buildings that were sheltering women and children and housing families destroyed, the ICC chose a crime that Russia has celebrated.

At a massive pro-war rally last month, the hosts showed off Ukrainian children.

The stadium watched propaganda of the children in their hometown, Mariupol, that was destroyed by Russian soldiers, and then hugging their supposed savior, who had helped force them at gunpoint across the border to Russia.

Russian TV has shown Ukrainian children stolen from their homeland receiving Russian documents.

And it's been blessed by the very top.

Last month, Russian President Vladimir Putin told Presidential Commissioner for Children's Rights Maria Lvova-Belova Russia was saving children from Eastern Ukraine.

VLADIMIR PUTIN, Russian President (through translator): The tragedy that is happening in Donbass affects our young children.

Unfortunately, that's true during the blatant aggression in Donbass against our people.

Of course, children have suffered.

NICK SCHIFRIN: Today, the ICC indicted Putin and Lvova-Belova.

JUDGE PIOTR HOFMANSKI, International Criminal Court (through translator): It is forbidden by international law for occupying powers to transfer civilians from the territory they live in to other territories.

Children enjoy special protection under the Geneva Convention.

NATALIYA GUMENYUK, The Reckoning Project: From some of the testimonies and also analytical reports and what we hear from the people, there is an attempt to indoctrinate those kids.

NICK SCHIFRIN: Nataliya Gumenyuk is the founding member of The Reckoning Project.

For "Vanity Fair," she and her team documented families whose children were kidnapped and then returned, including Yevhen Mezhevyi.

MAN (through translator): I put the children on the bus, hugged and kissed them.

GIRL (through translator): One man said he would be returned in seven years.

People said five or seven years.

BOY (through translator): They asked me again, do you want to join a foster family or an orphanage?

NICK SCHIFRIN: Tonight, Ukrainian President Volodymyr Zelenskyy called the indictment historic.

VOLODYMYR ZELENSKYY, Ukrainian President (through translator): Separating children from their families, depriving them of any opportunity to contact their relatives, throwing them in remote regions, all this is an obvious state policy of Russia.

NICK SCHIFRIN: So, could President Putin end up being arrested and put on trial by the International Criminal Court?

David Scheffer was U.S. ambassador at large for crimes issues during the Clinton administration.

He's now a senior fellow at the Council on Foreign Relations.

David Scheffer, welcome to the "NewsHour."

A senior official in the administration told me today that this would be the most consequential prosecution of international justice since the Nuremberg trials of Nazi leaders.

Why do you think this announcement is significant?

DAVID SCHEFFER, Former U.S.

Ambassador at Large For War Crimes: (AUDIO GAP) Secondly, bear in mind that indicting or issuing an arrest warrant against the head of state is always going to be a very, very significant development in international criminal justice.

And it has been done before over the last 30 years.

Many senior leaders, top leaders of countries have actually been indicted and brought to justice before international criminal tribunals.

And even before the International Criminal Court, al-Bashir of Sudan, Gadhafi of Libya, they were - - they were indicted while they were in power.

But the consequence, which is what Mr. Putin now faces, is that it does delegitimize the individual, so, first of all, certainly as an international pariah.

But, secondly, even domestically, it starts to erode at that person's power domestically.

And I think it'll be very interesting to watch how this affects the Russian opposition within Russia with respect to Mr. Putin's own fate in the near future.

NICK SCHIFRIN: We have never, of course, seen the ICC indict a head of state from a country so powerful as Russia.

Do you think this could lead one day to his arrest?

DAVID SCHEFFER: I think there's that possibility.

Even if it doesn't, he goes to his grave being an indicted fugitive of an international criminal tribunal.

But I do think 10, 15 years from now, perhaps Mr. Putin will not literally be in political power in Russia.

And, at that point, his exposure is even greater.

And the opposition, if they seize power in Russia, will see it to their advantage to actually turn him over to The Hague.

We certainly saw that in the Balkans with respect to Mr. Milosevic.

Ultimately, Serbia saw it to its advantage to turn him over to The Hague.

So, yes, it's different stakes.

It's Russia.

It's a nuclear power.

We have to always be very careful on that scale.

But it's not improbable that he would someday, maybe many years from now, actually face the bar of justice.

NICK SCHIFRIN: Today, the Kremlin responded by pointing out it's not a signatory to the ICC, and, therefore, an arrest is - - quote -- "null and void."

What legal argument does the ICC make to indict a head of state that is not a signatory?

DAVID SCHEFFER: Well, because, if the state parties to the Rome Statute agree that the sovereign immunity - - head of state immunity does not apply with respect to those who are issued -- subject to arrest warrants by the court.

In this case, Ukraine is not a state party to the court.

But under the terms of the Rome Statute of the ICC, it has invited the ICC to actually have jurisdiction with respect to the Russian invasion of Ukraine and the various atrocity crimes related thereto.

So there is jurisdiction for genocide, crimes against humanity and war crimes.

And, in this case, Mr. Putin would not have the defense of head of state immunity, because it's an international criminal tribunal.

It's not a Ukrainian court.

It's an international court, and that defense is not of effect before the International Criminal Court.

NICK SCHIFRIN: In some ways, today's charge is narrow.

The story that aired right before we started focused on the fact that it is the deportation of children from occupied territory.

The ICC had also been considering charges against Russia for indiscriminate bombing against civilian targets.

What's the significance of the ICC choosing this charge?

DAVID SCHEFFER: Well, this charge is actually low-hanging fruit, because they have been so transparent and self-incriminating in Russia about what they're doing with the Ukrainian children.

It's self-admitted by the leadership of Russia, and particularly these two individuals who were named today in arrest warrants.

But this will only be the beginning, because other crimes such as knocking out the power grid during the winter for the civilian population, the missile strikes throughout Ukraine hitting the civilian population and cultural sites, et cetera, all of that is to come.

This is just the first of, I would predict, a good number of arrest warrants that would name Putin, but also other individuals at the leadership, whether it be in the Foreign Ministry, the Defense Ministry, and the military forces at the command level.

NICK SCHIFRIN: David Scheffer, we will have to leave it there.

Thank you very much.

DAVID SCHEFFER: Thank you.