In Kiev, Ukrainians protest Russian action, vow to fight for their country

KIEV, Ukraine -- Ukraine's prime minister calls it a "declaration of war." The United States calls it an "invasion." Russia says it's protecting its people. What you call it depends on where you come from.

There are Russian forces in the Crimea region, and the White House says they effectively control the peninsula that makes up the southern portion of Ukraine. Secretary of State John Kerry is on his way to Ukraine Monday.

The U.S., European Union and NATO all say Russia is violating international law.

The question is: What can they do about it?

In pro-Western Kiev, what they're doing is protesting.

Protesters holding flags from the U.S., Germany and Italy arrive at Independence Square during a rally in Kiev Ukraine, Sunday, March 2, 2014. Emilio Morenatti, AP
Tens of thousands have gathered in the capital, demonstrating against Russia's actions. Anger, outrage and fear filled Kiev's Independence Square on Sunday.

Prime Minister Arseny Yatsenyuk warned that Russia's military intervention in Crimea has brought Ukraine to the brink of disaster.

"This is the red alert. This is not a threat. This is actually a declaration of war to my country," he said.

The newly formed Ukrainian government ordered a full military mobilization, putting all armed forces on high alert and calling on the hundreds of thousands of reservists to be ready to fight.

Thousands of demonstrators rallied against Russia's actions, calling President Vladimir Putin a dictator and a liar.

One sign read: "Putin: Hands off Ukraine."

In the place where they're still mourning those killed in demonstrations that brought the Russian-backed president down, activist Olesya Yeroshkina told us there's little appetite for more bloodshed.

"Of course I am worried. I don't want to have war, and I don't want more people to die here for our independence," she said.

Russian soldiers in control of Crimea
But every man of fighting age CBS News spoke to, like lawyer Oleg Pekatch, said they were ready to do just that.

"What Putin is doing right now in Crimea is absolute madness for everyone - for Putin, for Russia, for Russian people, for Europe, for the whole world," said Pekatch.

And if he is called on to fight, he says he will go.

"I'm more than sure," Pekatch said, smiling.

Nearly everyone told CBS News they were hoping - if not entirely convinced - that Russia would not push further into Ukraine after taking complete control of Crimea.

For all their patriotism, they are also aware that Ukrainian forces lack the hardware and firepower to match the Russian military.

Meanwhile, as many 20,000 Russian soldiers have been on the move across Crimea in the past 24 hours.

They've taken over without firing a shot.

A woman sweeps away the broken glass as two unidentified armed men guard the entrance to the local government building in downtown Simferopol, Ukraine, on Sunday, March 2, 2014. Ivan Sekretarev, AP
There are small pockets of resistance, such as those two bases where Ukrainian soldiers still loyal to the government in Kiev have barricaded themselves in.

But many Ukrainian security forces have switched sides - including the head of the navy in Crimea, Denis Berezovsky, who was only appointed by the government in Kiev on Saturday.

On Sunday, he announced in essence he would join the Russians.

A CBS News crew traveling to the Crimean provincial capital of Simferopol ran into a roadblock on the region's border. There, Ukrainian Interior Ministry troops had hoisted the Russian flag on their barricade.

They were backed up by local militia who stole the CBS News crew's body armor and helmets and told the crew to get out of there.

Kerry calls Russia's move "an incredible act of aggression"
The crew finally managed to enter Crimea by train.

Simferopol was very quiet. The crew saw some Russian soldiers standing guard around their armored vehicle near the provincial parliament. They seemed very relaxed. When asked how long they would be there, the soldiers smiled and said they didn't know.

Overall, the Russian soldiers have been welcomed by the large pro-Russian population. A big pro-Russian crowd in a Simferopol park sang patriotic Russian songs.

Anyone who is opposed to the Russian invasion - and there are thousands - is deeply worried. For the moment, they are keeping their heads down.

CBS News' Elizabeth Palmer in Simferopol contributed to this report.