Minutes later, large explosions were visible near Kharkiv, Ukraine’s second-largest city, and blasts were reported in Kyiv, the capital, and other parts of the country.

Ukraine’s Interior Ministry said that Russian troops had landed in Odessa and were crossing the border.

“The invasion has begun,” the ministry said in a statement.

Ukraine’s foreign minister, Dmytro Kuleba, said on Twitter that Mr. Putin had “started a full-scale war against Ukraine” and had begun shelling civilian cities.

“This is a war of aggression,” he wrote on Twitter. “Ukraine will defend itself and win. The world must act and stop Putin. It is time to act — immediately.”

Evoking the NATO bombing of Yugoslavia in 1999 and the American invasion of Iraq in 2003, Mr. Putin cast his action as a long-overdue strike against an American-led world order that he described as an “empire of lies.”

Even as he spoke, the United Nations Security Council held an emergency meeting imploring him not to invade.

Mr. Putin said he was acting after receiving a plea for assistance from the leaders of the Russian-backed separatist territories formed in eastern Ukraine in 2014 — a move that Western officials had predicted as a possible pretext for an invasion.

Mr. Putin also described the operation as a response to a “question of life or death” that he said Russia was facing as a result of the eastward expansion of the NATO alliance — which Ukraine has aspired to join.

“This is that red line that I talked about multiple times,” Mr. Putin said. “They have crossed it.”

The operation’s goal, Mr. Putin said, was “to defend people who for eight years are suffering persecution and genocide by the Kyiv regime,” citing the false accusation that Ukrainian forces had been carrying out ethnic cleansing in separatist regions of eastern Ukraine.

In bellicose language, Mr. Putin also issued what appeared to be a warning to other countries.

“Anyone who tries to interfere with us, or even more so, to create threats for our country and our people, must know that Russia’s response will be immediate and will lead you to such consequences as you have never before experienced in your history,” Mr. Putin said. “We are ready for any turn of events.”

In a statement, President Biden placed responsibility for the conflict squarely on Mr. Putin’s shoulders.

“President Putin has chosen a premeditated war that will bring a catastrophic loss of life and human suffering,” Mr. Biden said. “Russia alone is responsible for the death and destruction this attack will bring, and the United States and its allies and partners will respond in a united and decisive way. The world will hold Russia accountable.”

He added that he would address the American people on Thursday about “further consequences” the United States and its allies would impose on Russia.

Ukraine’s Foreign Ministry: “This is an act of war”

A spokesperson for Ukraine’s Ministry of Foreign Affairs described Russia’s military action Thursday as an “act of war” in a statement posted to Facebook.

“This is an act of war, an attack on sovereignty and territorial integrity of Ukraine, a gross violation of the UN Statute and the fundamental norms and principles of international law,” spokesperson Oleg Nikolenko said in the statement.

Nikolenko said Russian troops had carried out strikes on “peaceful” Ukrainian cities, in an offensive that aimed to “destroy the state of Ukraine, seize Ukrainian territory by force, and establish occupation control.”

Call for help: Nikolenko urged the international community to “act immediately,” requesting new sanctions be applied to Russia and military equipment to support Ukraine’s’ defense capabilities.

“Lives and security not only of the Ukrainian citizens, but also on the security of the citizens of Europe and the future of the world order depends on our united response,” the statement added.