Ukraine's authorities plan to launch a "full-scale anti-terrorist operation" involving the army against pro-Russian separatist militants, the acting president said on Sunday.

Oleksander Turchinov said in a televised address to the nation that Russia was waging a war against Ukraine by sowing disorder in the east of the country, but he offered not to prosecute any militants who gave up their weapons by Monday morning.

Referring to the death of a state security officer and the wounding of other members of law-enforcement bodies in an earlier clash with pro-Russian militants near the town of Slaviansk, he said: "The blood of Ukrainian heroes has been shed in a war which the Russian Federation is waging against Ukraine."

"The aggressor has not stopped and is continuing to sow disorder in the east of the country," he said, referring to a rash of attacks on state buildings by pro-Russian militants in towns in Russia-speaking areas of the east.

Kiev authorities say the separatists rebellions have been inspired and directed by the Kremlin, a charge Moscow denies.

"The National Security and Defense Council has decided to launch a full-scale anti-terrorist operation involving the armed forces of Ukraine," he declared.

"We will not allow Russia to repeat the Crimean scenario in the eastern regions of the country," referring to Moscow's annexation of the peninsula following its take-over by pro-Russian militants.

The Russian foreign ministry responded to Turchinov's announcement on Sunday, calling the decision to mobilize the Ukrainian army "an illegal order." According to Interfext news agency, the ministry stated that it seeks to put Ukrainian actions "high on the UN Security Council agenda," calling on the West to get its "allies in Ukraine under control" if it hopes to prevent a civil war.

Anti-Kremlin demonstration in Moscow

Later on Sunday, about 10,000 people turned out in Moscow for an anti-Kremlin rally to denounce Russian state television's news coverage, particularly of the crisis in neighboring Ukraine.

In promoting the Kremlin line, state television has portrayed the new pro-Western government in Ukraine as a "fascist junta" under the control of the U.S. government and determined to oppress Russian speakers in eastern Ukraine. The broadcasts have taken on a harsh anti-American tone.

Some of those who took part in the demonstration, called a "March of Truth," carried blue and yellow Ukrainian flags. One woman, wearing a traditional Ukrainian wreath of flowers on her head, held up a sign with President Vladimir Putin's picture and the words: "Stop lying."

Among those who spoke to the crowd was Andrei Zubov, a history professor who was fired from one of Moscow's most prestigious universities last month after criticizing Russia's military intervention in Ukraine's Crimean Peninsula. Zubov argued against the annexation of Crimea by comparing it with Nazi Germany's annexation of Austria on the eve of World War II.

Zubov told the crowd that by lying to the Russian people on television, the government was leading the country toward "an abyss."

New sanctions

The United States is prepared to step up sanctions against Moscow if pro-Russian military actions in eastern Ukraine continue, the U.S. envoy to the United Nations said on Sunday.

Pro-Russian activists seized government buildings on Saturday in the eastern town of Slaviansk, about 150 km from the Russian border. Ukrainian security forces were trying to oust the activists, who set up barricades on the outskirts of the city.

The American ambassador to the UN, Samantha Power, said on ABC's "This Week" that the latest events in Ukraine bore "the telltale signs of Moscow's involvement."

She said sanctions already imposed by Washington have had an impact: the Russian ruble has fallen to an all-time low, the country's stock market has depreciated by 20 percent and investors are fleeing the country.

"The president has made clear that, depending on Russian behavior, sectoral sanctions in energy, banking, mining could be on the table, and there's a lot in between," Power said.

"I think we've seen that the sanctions can bite, and if actions like the kind we've seen over the last few days continue, you're going to see a ramping up of those sanctions."

The sanctions have been the most visible sign of U.S. anger at Russia's annexation of the Crimea region in southern Ukraine last month, reflecting the deepest plunge in U.S.-Russian relations since the Cold War.

Ukraine now faces a rash of rebellions in the east that it says are inspired and directed by the Kremlin.

Asked on ABC if Russian President Vladimir Putin wants to seize eastern Ukraine, Power said his actions "give credence to the idea."

Though Russians are insisting that is not what Moscow wants, she said, "Everything they're doing suggests the opposite."

NATO described the appearance in eastern Ukraine of men with specialized Russian weapons and identical uniforms without insignia -- as previously worn by Moscow's troops when they seized Crimea -- as a "grave development."

Power said the rebellion has "all the telltale signs of what we saw in Crimea: It's professional, it's coordinated, there's nothing grassroots-seeming about it. The forces are doing in each of the six or seven cities that they've been active in exactly the same thing."

Republican Senator John McCain, a frequent critic of U.S. policy on Ukraine, said on CBS that the Obama administration's failure to punish Russia over Crimea has only emboldened Putin.

"The question is now, What do we do and what does he do?" McCain said on "Face the Nation." "It's obvious that he is encouraged by the fact that we sanctioned a few people and suspended -- didn't even throw him out -- of the G8."

McCain repeated his calls for tougher sanctions and for giving Ukrainians light weapons so they can defend themselves.

"They didn't fight in Crimea," he said. "But if he starts moving in further encroachment in this way into eastern Ukraine, they will fight."

The United States on Friday imposed sanctions on a Crimea-based gas company, Chernomorneftegaz, effectively putting it off limits to Russia's state-controlled Gazprom, which was expected to bid for a stake in the company.

The move, along with penalties on six Crimean separatists and a former Ukrainian official, is the third round of U.S. sanctions since the Ukraine crisis erupted.