Russia's Foreign Ministry has expressed concern at what it terms the "lawlessness" affecting Russians and Russian-speakers in eastern Ukraine.
The ministry's statement Monday an incident in Kharkiv on March 8, during which it says masked men linked to the ultranationalist Right Sector group -- in "connivance" with the new government in Kyiv -- opened fire on peaceful protesters.
Kharkiv police acknowledged a minor incident but said the only link to Right Sector came from an anonymous phone call.
The Russian Foreign Ministry also complained that police in Dnepropetrovsk had detained seven Russian journalists.
The ministry's statement expressed "surprise at the shameful silence of our Western partners, rights organizations, and foreign media" over the incidents.
Ukraine's government and Western leaders accuse Moscow of distorting the facts to portray protesters who toppled President Viktor Yanukovych as violent extremists.
Reports say Yanukovych will make a public statement at midday on March 11.
Yanukovych is due to deliver his remarks from Russia's southern city of Rostov-on-Don, marking only his second public statement since he fled Ukraine last month during antigovernment unrest.
On February 28, also in Rostov-on-Don, Yanukovych said he was still the legitimate president of Ukraine and dismissed the country's current authorities as "fascist thugs."
In a show of support for the new government in Kyiv, U.S. President Barack Obama will meet Ukraine's new Prime Minister Arseniy Yatsenyuk at the White House on March 12. Yatsenyuk will address the UN Security Council about the crisis on March 13.
Meanwhile, Obama and his Chinese counterpart, Xi Jinping, discussed the situation in Ukraine in a phone conversation late on March 9. A White House statement said the two leaders agreed on the importance of upholding Ukraine's sovereignty and territorial integrity after the occupation of Crimea by Russian forces.
It said the presidents have a shared interest in reducing tensions and finding a peaceful resolution to the dispute.
In Kyiv, former Russian oligarch Mikhail Khodorkovsky told a group of university students that Moscow's actions in eastern Ukraine are ruining the traditionally friendly ties between the two peoples.
Khodorkovsky expressed support for the new Ukrainian government, saying a "revolution of justice" had brought it to power. He said "Ukraine must become a European state."
On March 9, Khodorkovsky addressed thousands on Kyiv's Independence Square, saying "Russian propaganda lies as always" and blaming Russian officials for fabricating stories about fascists and Nazis taking advantage of the situation in Ukraine.
He said there are people in Russia who oppose the occupation of Crimea.
"I want you to know -- there is a completely different Russia out there. There are people who kept coming to demonstrate against war in Moscow despite arrests and long years in prison they are facing. There are people [in Russia] for whom friendship between Ukrainian and Russian peoples is more important than their personal freedom," Khodorkovsky said.
The former Yukos oil chief was arrested in 2003 and imprisoned on tax evasion and other charges. He was amnestied in December.
Demonstrations from pro-Ukrainian and pro-Russian groups were expected again in eastern Ukraine on Monday. The two groups held rival rallies on March 9.
Pro-Russian activists attacked pro-Ukrainian activists with clubs and whips in the Crimean city of Sevastopol.
There were also reports of pro-Ukrainian demonstrators beating pro-Russian demonstrators at at least one rally on March 9 in eastern Ukraine.
And at least five Ukrainian activists and journalists opposed to Russia's invasion of Crimea have gone missing in the peninsula.
With reporting by Reuters, BBC, CNN, and AP