Putin may be committing war crimes, but do the allegations have any teeth?

The International Criminal Court has opened an investigation into the war in Ukraine as pressure mounts to prosecute Russian President Vladimir Putin as a war criminal. 

The case against Putin could come together quickly as the list of alleged violations grows: the bombing of a maternity hospital, the shelling of civilian targets and an attack on a nuclear power plant that raised the specter of a nuclear disaster in the heart of Europe. 

But a conviction could prove elusive. The International Criminal Court, which the U.S. is not part of, has a track record of 10 convictions over two decades. 

"The first way that they can build it — and it may be sufficient in this case — they can look at the pattern of the attack," Stephen Rapp, a former U.S. ambassador at large for war crimes, told CBS News senior investigative correspondent Catherine Herridge. 

Rapp, who has built cases against dictators and sought accountability for genocide, said Putin would be seen as "an international pariah" if there is a war crimes designation against him. 

"It also means that he can't travel anywhere, no more summits, because he'd be putting himself in danger," Rapp said. 

Securing justice in the court does not happen quickly. 

The court had to pull the arrest warrant for Libyan leader Muammar al-Gaddafi after he was executed by his own people. Syrian President Bashar Al-Assad remains in power nearly a decade after he allegedly used chemical weapons against Syrians. 

Even though the U.S. is not part of the International Criminal Court, a National Security Council spokesperson told CBS News that the U.S. is already collecting evidence of alleged war crimes and human rights abuses that could be used in a criminal prosecution. 

The U.S. Embassy in Kyiv called the attack on the Zaporizhzhia nuclear power plant a "war crime." But hours later, the White House dialed back the language. 

"We have not made conclusions, it's a legal review and a process that goes through at the administration," White House Press Secretary Jen Psaki said. 

Rapp said the bar is "very high" to prove that war crimes have been committed, but "given the intensity of this campaign and the civilian destruction, I think that can be developed in a matter of weeks." 

Matthew Kroenig, who worked the Russia and nuclear portfolios for the intelligence community under the Bush, Obama and Trump administrations, told CBS News there's a rising threat from Russia's stockpile of lower-yield weapons known as tactical nukes. 

"These are weapons that would be used not for, say, attacking Washington or New York, but for winning a battle on the field in Ukraine," Kroenig said. 

Use of tactical nuclear weapons against civilians would be "a war crime of the highest order," he said. 

This week, intelligence officials warned of a Russian policy called "escalate to deescalate," which means the use of tactical nuclear weapons on the battlefield to intimidate an adversary. 

"I think before he lost the war, he would try to use nuclear weapons to try to pull victory from the jaws of defeat," Kroenig said of Putin. "I think the risk of nuclear war is still low. But I think the risk is higher now than any time we've seen in recent years."