Putin declared that Western actions were driving Ukraine into anarchy and warned that any sanctions the West might place on Russia for its actions there will backfire.
"We aren't going to fight the Ukrainian people," Putin said, adding that Russian military maneuvers involving 150,000 troops near Ukraine's border had been planned and were unrelated to the current situation in Ukraine. He ordered the troops back to their bases Tuesday.
The U.S., meanwhile, announced a $1 billion aid package in energy subsidies to Ukraine, which faces a looming financial disaster. NATO members met in Brussels and said the alliance would hold talks Wednesday with Russian officials about Ukraine. World markets rose, buoyed by Putin's apparent efforts to de-escalate tensions.
"We are going to do our best (to help you). We are going to try very hard," Kerry said in Kiev. "We hope Russia will respect the election that you are going to have."
Tensions remained high in Crimea, with troops loyal to Moscow firing warning shots to ward off protesting Ukrainian soldiers. Heavily armed Russian forces have taken over the strategic peninsula, surrounding its ferry, military bases and border posts. Two Ukrainian warships remained anchored in the Crimean port of Sevastopol, blocked from leaving by Russian ships.
The new Ukrainian leadership in Kiev, which Putin does not recognize, has accused Moscow of a military invasion in Crimea, which Putin denies.
"Those unknown people without insignia who have seized administrative buildings and airports ... what we are seeing is a kind of velvet invasion," Russian military analyst Alexander Golts told The Associated Press in Moscow.
Yet world markets recovered from their fright over Ukraine, clawing back a large chunk of Monday's stock losses, while oil, gold, wheat and the Japanese yen gave back some gains. In New York, the Dow Jones Industrial Average surged 200 points Tuesday on the news that Putin had pulled troops away from Ukraine's border.
"Confidence in equity markets has been restored as the standoff between Ukraine and Russia is no longer on red alert," said David Madden, market analyst at IG.
Speaking from his residence outside Moscow, Putin said he still considers Viktor Yanukovych to be Ukraine's president and hopes that Russia won't need to use force in predominantly Russian-speaking eastern Ukraine.
Putin also insisted that the Russian military deployment in Crimea has remained within the limits set by a bilateral agreement on a Russian military base there. He said Russia had no intention of annexing Crimea, but insisted its residents have the right to determine the region's status in a referendum later this month.
Putin accused the West of using Yanukovych's decision in November to ditch a pact with the EU in favor of closer ties with Russia to encourage the months of protests that drove him from power and put Ukraine's future in turmoil.
"We have told them a thousand times 'Why are you splitting the country?'" he said.
Yet he acknowledged that Yanukovych has no political future and said Russia gave him shelter only to save his life. Ukraine's new government wants to put the fugitive leader on trial for the deaths of over 80 people during protests in Kiev.
At the House of Commons in London, British Foreign Minister William Hague rejected Putin's arguments.
"The suggestion that a president who has fled his country then has any authority whatsoever to invite the forces of a neighboring country into that country is baseless," he told U.K. lawmakers.
Ukraine's dire finances were a key issue in the protests that drove Yanukovych from power. On Tuesday, Russia's state-controlled natural gas giant Gazprom said it will cancel a price discount on gas it sells to Ukraine. Russia had offered the discount in December as part of Russian help for Ukraine. Gazprom also said Ukraine owes it $1.5 billion.
Ukraine's finance minister, who says the country needs $35 billion to get through this year and next, was meeting with International Monetary Fund officials.
Crimea still remained a potential flashpoint. Troops who had taken control of the Belbek air base in Crimea fired warning shots into the air Tuesday as around 300 Ukrainian soldiers who previously manned the airfield demanded their jobs back.
About a dozen troops warned the Ukrainians, who were marching unarmed, not to approach. They then fired several warning shots into the air and said they would shoot the Ukrainians if they continued toward them. The Ukrainians identified the gunmen as Russian and their vehicle had Russian military plates.
Part of the compound was still being held by Ukrainians.
"We are worried. But we will not give up our base," said Capt. Nikolai Syomko, an air force radio electrician holding an AK-47 and patrolling the back of the compound. He said the soldiers felt they were being held hostage, caught between Russia and Ukraine.
"They have shown restraint, despite the invasion of the Ukrainian homeland and a Russian government that has chosen intimidation," Kerry said of the Ukrainian soldiers.
The new Ukrainian government says troops that have overtaken Belbek and other Ukrainian military bases across Crimea were Russian. Putin denied it, saying the men were self-defense forces answering to Crimea's pro-Russian regional government.
Putin said Ukraine's 22,000-strong force in Crimea has dissolved and its arsenals have fallen under the control of the local government. Those officials claimed Tuesday that 5,500 Ukrainian soldiers had switched allegiances from Kiev to them. They were also seeking to move up a vote planned for March 30 on the region's status.
Ukraine's prime minister placed the blame for the current crisis with Russia squarely on the Kremlin, but expressed hope that a negotiated solution could be found. Prime Minister Arseniy Yatsenyuk told a news conference on Tuesday that both governments were talking again, albeit slowly.
"We hope that Russia will understand its responsibility in destabilizing the security situation in Europe, that Russia will realize that Ukraine is an independent state and that Russian troops will leave the territory of Ukraine," he said.
Russia is demanding the implementation of a Western-sponsored peace deal that Yanukovych signed with the opposition last month that set a new Ukrainian presidential election no later than December. Yanukovych fled the capital hours later and ended up in Russia, and the Ukrainian parliament then set the presidential vote for May 25.
The EU's 28 heads of state and government will hold an emergency meeting Thursday to decide whether to impose sanctions against Russia.
John Herbst, a former U.S. ambassador to Ukraine now at the Center for Complex Operations at the National Defense University, told the AP it was a critical time for Europe.
"It's a breach of international law, of national sovereignty, by a major power," Herbst said about Russia's actions in Crimea. "We haven't seen such a breach in Europe since the Nazis."
Sullivan reported from Crimea. Ivan Sekretarev in Sevastopol, Juergen Baetz in Brussels and Raul Gallego in Crimea contributed to this report.