Russian warplanes have entered Ukrainian airspace several times in the last 24 hours, the Pentagon announced Friday.
U.S. officials called on Russia to cease the operations, said Army Col. Steve Warren, a Pentagon spokesman.
"We call upon the Russians to take immediate steps to de-escalate the situation," Warren said.
Army Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, spoke with his Russian counterpart on Thursday, but details of their conversation were not released. Defense Secretary Chuck Hagel has tried, without success, to contact Russia's defense minister.
Ukraine's air defenses are old but still potent enough, under the right circumstances, to take down Russian aircraft, said Michael O'Hanlon, a military analyst at the Brookings Institution. In fact, drawing fire might be Russia's intent by entering Ukraine's airspace.
"I don't put a deliberate provocation, in order to create a pretext for response and invasion, past Putin at this point," O'Hanlon said.
The U.S. response to such a move, O'Hanlon said, would be limited, perhaps the sale of arms or sharing intelligence.
The violation of Ukraine's airspace follows war games that Russian troops began near the border. About 40,000 Russian troops have massed there, according to the Pentagon. Last month, Russian troops seized key facilities on the Crimean peninsula and annexed it.
Tensions in the region have escalated steadily since then. Russian-backed separatists have seized government facilities in eastern Ukraine, prompting Ukrainian forces to try to evict them. Several people have been killed in those clashes.
Earlier this week, the Pentagon deployed 600 paratroopers to Poland and three other Baltic states to reassure NATO allies in the region about the U.S. commitment to their defense.
Ukrainian Prime Minister Arseniy Yatsenyuk charged Friday that Moscow "wants to start World War III" by seeking to take over Ukraine militarily and politically.
"Russia behaves as an armed gangster, but the time will come when the gangster will be hit in the face," he said at a government meeting Friday. "The aggressive efforts of the Russian military on Ukraine's soil will lead to a conflict on European soil."
"The world has not yet forgotten World War II, but Russia already wants to start World War III," Yatsenyuk said.
The prime minister accused Russia of organizing the unrest in Ukraine's east to sabotage Ukrainian presidential elections, scheduled for May 25 when the country will vote on a replacement for former president Viktor Yanukovych, who was ousted following street protests in February.
Over the past two weeks armed pro-Russia protesters have taken over some key administrative buildings in Ukraine's eastern Donetsk region, demanding a referendum on the region joining Russia.
Ukrainian officials have taken back some buildings in ongoing anti-terrorist operations that resumed Tuesday after separatists were accused of murdering a pro-Kiev local official, whose body was found near the separatist-controlled city of Slovyansk.
In the latest incident on Friday, a Ukrainian military helicopter exploded at an airfield in Ukraine's east after it was shot at by a grenade-launcher, said the country's Defense Ministry.
Pro-Russian protesters had stormed the same airfield April 15. At the time, the Ukrainian army pushed them back, wounding three protesters, to the dismay of some 300 locals who blamed the army for opening fire.
The Defense Ministry is investigating the incident, but has not released information on who they think is behind the attack. Nobody was killed in the incident, which came after Ukrainian law enforcers killed five separatists, while attacking their roadblock in the east.
In another development, a Ukrainian foreign ministry spokesman, Yevhen Perebyinis, said at a briefing on Friday that contact had been lost with members of a military verification mission of the Organization for Security and Cooperation in Europe (OSCE) in Donetsk region, in the east.
Perebyinis said that "according to preliminary report, they could be captured by terrorists," Interfax Ukraine reports. The OSCE mission was sent into disputed areas to try to calm tensions. There have been no confirmation of the report that the members of the team may have run into trouble.forts of the Russian military on Ukraine's soil will lead to a conflict on European soil."
Meanwhile, Russia announced new military exercises Thursday involving ground and air forces near its border with Ukraine.
Russian Foreign Minister Sergey Lavrov accused the West of plotting to control Ukraine to bolster its own interests in the region.
"The West wants -- and this is how it all began -- to seize control of Ukraine because of their own political ambitions, not in the interests of the Ukrainian people," Lavrov said.
As tensions mounted, seven people were injured early Friday when a hand grenade was tossed at a checkpoint manned by pro-Ukrainian activists outside the Black Sea port of Odessa in southeastern Ukraine.
Local police spokesman Volodymyr Shablienko said unknown men threw the explosive device at a checkpoint set up by local authorities and activists.
Odessa residents have built several checkpoints outside of the city in an effort to block pro-Russian separatists entering from Moldova's breakaway territory of Transdniestria. The enclave, which declared indeendence in the early 1990s, is located about 50 miles west of Odessa. It is home to Russian peacekeepers and Russian troops guarding a cache of Soviet-era arms.
A senior official traveling in Asia with President Barack Obama said he is likely to call European leaders Friday to discuss the possibility of further economic sanctions on Russia. The official spoke on condition of anonymity because there had been no official announcement.
Secretary of State John Kerry charged on Thursday that Russia is not abiding by last week's Geneva agreement to de-escalate the crisis in Ukraine. Russia, he said, "has refused to take a single step in the right direction."
"If Russia continues in this direction, it will be not just a grave mistake, it will be an expensive mistake," he told reporters at the State Department. "The world will make sure costs for Russia will only grow."
In another development, Ukraine's State Security Service announced Friday that it had arrested two Ukrainians allegedly working for Russian intelligence services. One of the arrested was an officer of the Interior Ministry's Internal Troops, who was assigned with getting information on internal troop locations.
The internal troops are under the control of the Interior Ministry and are the main force behind the counter-terrorist operation lead by Ukraine's government in the east against armed separatists. The operation was suspended for a few days after Ukraine and Russia agreed on measures to deescalate tensions in the region in Geneva April 17.
Russia has hinted it may send troops into the region to protect ethnic Russians, but a new poll published by the Washington-based International Republican Institute showed that 69% of Ukrainians living in the country's troubled east are against Russian troops entering Ukraine.
Some in the east are also frustrated with a perceived lack of progress against the pro-Moscow protests.
"I say -- if we have a state, it must restore order, and not leave us one on one with these people," said Natalia Afanasieva, who lives in Horlivka, a city the Donetsk region."
Contributing: Associated Press