• Russia launched an unprecedented invasion of its neighbor Ukraine in the early hours of Thursday morning.
• Russian President Vladimir Putin issued a chilling warning to the West, saying any country which tried to "interfere" would face immediate consequences.
• U.S., Europe and Ukrainian officials have condemned the attack with Ukraine's foreign minister, Dmytro Kuleba, calling for "heavy sanctions" on Moscow.

Russia launched an unprecedented invasion of its neighbor Ukraine on Thursday, with military assaults on several key Ukrainian cities including its capital, Kyiv.

The attack on Ukraine is taking place both on the ground and by air, with reports that Russian forces have breached the Kyiv region. Explosions have also been heard in the cities of Odessa, Kharkiv and Mariupol, and there are reports of fighting and fatalities in other parts of the country. 

Officials said the offensive had already killed dozens of soldiers and several civilians as of Thursday afternoon.

Follow our live updates here: Explosions and sirens in Kyiv as Russia invades Ukraine

Stocks fell sharply on the news of the invasion with investors fleeing for safe-haven assets, while global energy prices jumped to multi-year highs.

Russia began attacking various positions across the country early Thursday local time after Russian President Vladimir Putin announced that Russia would carry out a "special military operation" in Ukraine.

Its goal, Putin said, was what he called "the demilitarization" of Ukraine. He said Russia's plans do not include the occupation of Ukrainian territories, saying "we are not going to impose anything on anyone by force."

There's little evidence of military aggression from Ukraine, and Russia's claims to the contrary are seen by many as a pretext for justifying an invasion.

On Thursday on Twitter, Ukrainian President Volodymyr Zelenskyy called for "an immediate end to Putin's war against the world" and said "we are building an anti-Putin coalition" without elaborating further. He also called for immediate sanctions on Russia as well as "defense and financial support" saying "the world must force Russia into peace."

The Kremlin issued more statements later Thursday, saying Putin would decide how long the military operation would last "based on its progress and aims." Putin's spokesman, Dmitry Peskov, also told reporters Ukraine needs to "ideally" be "liberated" but that "nobody is talking about the occupation of Ukraine," saying that word was "unacceptable," according to Reuters.

Speaking Thursday, NATO Secretary-General Jens Stoltenberg said that "in the coming days and weeks, there will come even more [soldiers], so we will further increase and we are increasing our presence in the eastern part of the alliance," although he also repeated that, as it stands, NATO had no plans to send its troops into Ukraine.

The comments came as Ukraine's military said Russia had attacked it with more than 30 strikes on civilian and military infrastructure, including the use of Kalibr cruise missiles.

Close followers of Russian politics believe Putin wants to destabilize Ukraine's pro-Western government and to instead install a pro-Russia regime there.

U.S., Europe and Ukrainian officials have condemned the attack with Ukraine's foreign minister, Dmytro Kuleba, calling for "heavy sanctions" on Moscow.

President Joe Biden on Thursday morning convened a meeting of the National Security Council — the third this week — to discuss the U.S. response to the attacks. He will also meet virtually with G-7 members on Thursday ahead of an address to the nation.

It's unclear, as yet, whether Western powers will deploy military means to stop Putin. Several countries, including the U.S. and U.K., have already sent weapons to Ukraine to help it defend itself. Ukraine's foreign minister has called for more weapons and financial and humanitarian assistance.

Putin issued a chilling warning to the West when he announced the military operation against Ukraine, saying any country that tried to "interfere" would face immediate consequences.

What's going on?

The situation in Ukraine is rapidly deteriorating and developments are difficult to confirm, but there are already reports of casualties.

Oleksiy Arestovych, an advisor to Ukraine's Presidential Office, told NBC News that the government had received confirmation that "a couple of dozen" Ukrainian soldiers had died, mostly from the airstrikes and rocket strikes in the morning.

Ukraine's armed forces have also claimed they have destroyed some Russian aircraft and that a number of Russian soldiers have died during fighting Thursday.

Operational information released by the General Staff of the Armed Forces of Ukraine on Facebook stated that four Russian tanks were "burned" in the Kharkiv area, in northeast Ukraine near the Russian border, but also that "heavy battles" were taking place in the area.

Ukraine's Joint Forces Command reported that about 50 Russian "occupiers" were killed in the Shchastya area in Luhansk, eastern Ukraine, earlier on Facebook. Ukrainian forces had "stopped the opponent" in Chernihiv, a city in northern Ukraine, according to a later Facebook post.

Ukraine's State Emergency Service has also reported a fire at a residential building in Chuguiv in the Kharkiv region, that it said was due to shelling. A minor had died during the incident and other people were injured, the service said.

Earlier, Ukrainian police said that six people had been killed during bombing of Podilsk in the Odessa region, with a further seven people wounded and 19 people missing, which was confirmed by NBC News.

A video has also been released by the Ukrainian Interior Ministry which appeared to show military vehicles crossing the border into Ukraine. The ministry said the video was filmed early Thursday morning at the border with Crimea, which Russia annexed from Ukraine in 2014.

Some of the vehicles were seen to have a "Z" mark, which has been a feature of Russian military vehicles that had been massing along the border with Ukraine in recent months although it cannot be definitively said that the vehicles are Russian.

NBC News has also been able to verify a video showing explosions over the skyline of Kharkiv.

There are reports of the center of Kyiv being largely deserted on Thursday and of large traffic jams forming on roads out of the city as people try to leave for safety. Western officials have warned there could be a wave of migration into Eastern Europe as Ukrainians flee the conflict.

Ukraine's defense minister, Oleksii Reznikov, posted a message on Facebook in which he called upon able Ukrainians to take up arms against Russian forces.

"Anyone who is ready and able to hold weapons" can now join the Territorial Defense Forces, he said, adding that to get weapons, Ukrainians needed to contact "brigades and battalions directly in your region. You only need to have a passport," to sign up, he said.

"The enemy attacks, but our army is unbreakable," Reznikov wrote, noting that Ukraine had gone "into total defense mode."

—CNBC's Karen Gilchrist contributed to this report.