NATO Secretary-General Anders Fogh Rasmussen has accused Russia of engaging in "direct military operations" in Ukraine and dismissed Moscow's "hollow denials" of involvement.
Rasmussen was speaking to reporters in Brussels on August 29 after an emergency NATO meeting to discuss the Ukraine crisis.
He said that "it is now clear that Russian troops and equipment have illegally crossed the border," part of a "dangerous pattern" to destabilize Ukraine and a "blatant violation" of its sovereignty.
Rasmussen said Moscow had supplied pro-Russian separatists with tanks, armor, artillery, and rocket launchers and had fired on Ukrainian troops from Russian territory and Ukrainian soil.
Russian Foreign Minister Sergei Lavrov said earlier on August 29 that the West had failed to prove its claims of Moscow's military involvement in Ukraine and dismissed them as "conjecture."
Rasmussen also said NATO's 2008 assurance that Ukraine will one day join the alliance if it wishes still stands.
His comment came in response to an announcement by Ukrainian Prime Minister Arseniy Yatsenyuk that the government would ask parliament to set the country on a path toward NATO membership, a move certain to anger Russia.
Yatsenyuk was speaking in Kyiv while government troops remain locked in a five-month-old conflict with pro-Russian separatists in its eastern regions.
He said, however, that the basic aim of Ukrainian foreign policy remains to become a member of the European Union.
If passed, Yatsenyuk said the relevant bill would forbid Ukraine from making a decision on membership in "any other economic, political, or other unions" that would prevent the country from eventually joining the European Union.
Putin: Russians. Ukrainians 'One People'
Russian President Vladimir Putin, meanwhile, has called the fighting in eastern Ukraine a tragedy and compared it to the World War II Nazi siege of Leningrad.
"Small villages and large cities surrounded by the Ukrainian Army, which is directly hitting residential areas with the aim of destroying the infrastructure," Putin said. "It sadly reminds me the events of World War II, when German fascist...occupants surrounded our cities."
Putin, speaking at a youth camp outside Moscow on August 29, also said he believed Ukrainians and Russians are "practically one people."
"People who have their own views on history and the history of our country may argue with me," Putin said, "but it seems to me that the Russian and Ukrainian peoples are practically one people."
He said Kyiv must engage in "substantial, meaningful talks" with the rebels in an effort to end the fighting.
Officials in Kyiv "don't want to speak on substance, that is the problem," he said.
Putin also said Russia had no desire to get involved in large-scale conflicts, "but naturally, we should always be ready to repel any aggression toward Russia."
"Our partners, no matter what state their countries are in and whatever foreign-policy concept they stick to, must understand that it is better not to mess with us," he said.
On August 28, a senior NATO official said at least 1,000 Russia troops were operating in Ukraine and the alliance released what it said were satellite photos of Russian self-propelled artillery units moving last week.
"The hand from behind is becoming more and more overt now," Brigadier General Nico Tak said.
Tak said that Russia's ultimate aim was to stave off defeat for the separatists and turn eastern Ukraine into a "frozen conflict" that would destabilize the country indefinitely.
Speaking in Moscow on August 29, Russian Foreign Minister Lavrov said, "We have not been presented with any proof of...an invasion."
Lavrov said Russia wanted an end to the bloodshed and the start of a "true national dialogue" in Ukraine. He accused Western governments of reneging on commitments to work toward these goals.
Lavrov also said he believed Moscow and Kyiv have a "common understanding" on a second humanitarian aid convoy for eastern Ukraine. The first Russian convoy entered Ukraine last week without Kyiv's approval.
WATCH: Aleksandr Zakharchenko, the leader of pro-Russian separatists in the eastern Ukrainian city of Donetsk, has agreed to let encircled Ukrainian government troops leave the battlefield after Russian President Vladimir Putin called on militia forces to open "a humanitarian corridor."
Ukraine's military, meanwhile, has said a call by Putin for a "humanitarian corridor" to allow Ukrainian troops encircled in the east to withdraw proves Moscow's hand in the conflict.
In a statement, Ukraine's military said on August 29 that Putin's statement testifies to only one thing -- "[the separatists] are led and controlled directly from the Kremlin."
Putin issued a call earlier on August 29 urging rebels in what he termed "Novorossia" to open corridors to allow trapped Ukrainian troops to withdraw safely.
Novorossia, or New Russia, is a tsarist-era name for a broad strip of land encompassing most of southern Ukraine.
Putin's use of the term in the past has raised concerns the Kremlin may have designs on the entire area from the Russian border and the rebel-held southeastern city of Donetsk to Moldova's breakaway, pro-Russian Transdniester region in the west.
Control over this territory would cut Ukraine off from Crimea, which Moscow annexed in March, and give Russia access to the peninsula by land.
Putin's statement is believed to refer to Ukrainian troops who have been trapped near the strategic town of Ilovaysk, east of Donetsk, for almost a week.
Aleksandr Zakharchenko, a top rebel leader, told Russian television his forces would comply with Putin's request but said Ukrainian troops would have to leave their heavy armored vehicles and ammunition behind.
Obama: Russia Responsible
U.S. President Barack Obama has accused Russia of training, arming, and funding the rebels, saying at the White House on August 28, "We agree, if there was ever any doubt, that Russia is responsible for the violence in eastern Ukraine."
Obama said the new NATO images of Russian forces inside Ukraine made that plain to see. But he stopped short of calling Russian involvement in Ukraine an "invasion" and ruled out military action.
Obama said he had spoken with German Chancellor Angela Merkel and both leaders agreed Russia must face consequences for its actions.
Merkel said tougher sanctions against Russia would be considered on August 31 at an EU summit.
Obama said current sanctions against Moscow had already made Russia "more isolated than at any time since the end of the Cold War."
Obama also announced Ukrainian President Petro Poroshenko will visit the White House on September 18.
At an emergency session of the UN Security Council, Western representatives expressed outrage at Russia's actions in eastern Ukraine.
U.S. Ambassador Samantha Power said Russia "has manipulated. It has obfuscated. It has outright lied."
She said the United States will work with its G7 and European partners "to ratchet up the consequences on Russia."
France also warned of increased sanctions if the escalation continues.
Russian Ambassador Vitaly Churkin did not deny the Russian presence but said they were "Russian volunteers," echoing an earlier statement by a rebel leader.
WATCH: RFE/RL's Andrei Babitsky shot footage of fierce fighting on the streets of the eastern Ukrainian city of Donetsk on August 28. (WARNING: Graphic content, including dead bodies)
Earlier, Ukrainian officials said Russian troops, backed by tanks, had seized the border town of Novoazovsk.
Andriy Lysenko, a spokesman for Ukraine's security forces, said on August 28 that government forces had regrouped to defend Mariupol.
He also said Ukrainian troops had clashed with a Russian military reconnaissance patrol trying to cross into the Kherson region from the Crimean Peninsula.
Ukraine also said it had decided to reintroduce compulsory military service in the fall, but conscripts would not serve in the conflict zone.
In a new report, the UN said on August 29 that the conflict in eastern Ukraine has killed nearly 2,600 people since mid-April and noted "serious human rights abuses" including abductions and torture committed "primarily" by pro-Russian separatists.
With reporting by AP, AFP, and Reuters