It is President Putin's first statement on the crisis since Russian troops poured into Crimea. Photo: BBC

But Russia reserves the right to use "all means" to protect citizens in the east of the country, Mr Putin said.

He denied Russian troops had besieged Ukrainians based in Crimea - they were pro-Russian "self-defence" forces.

Mr Putin called the toppling of President Viktor Yanukovych in the capital Kiev an "anti-constitutional coup and armed seizure of power".

Crimea remains a major focus of the crisis, as troops in what appear to be Russian uniforms surround Ukrainian military bases and other installations. Russia is de facto in control of the peninsula.

Tensions were especially high at Belbek airbase near Sevastopol, the port city which is the base of Russia's Black Sea Fleet. Pro-Russian forces fired warning shots in the air, and Ukrainian troops later marched away from the base.

Meanwhile, two Ukrainian warships are reported to be blocked by a Russian ship in the port of Sevastopol.

There is intense diplomatic activity aimed at defusing the crisis.

US Secretary of State John Kerry has arrived in Kiev to meet Ukraine's new leaders and show support for the country's sovereignty.

And Russian Foreign Minister Sergei Lavrov is expected to meet the EU foreign policy chief, Catherine Ashton, in the Spanish capital Madrid.

Ukraine 'chaos'

Mr Putin said "militants" had plunged Ukraine into "chaos". He also said Ukrainian "nationalists" and "anti-Semites" were roaming the streets of Kiev and other cities.

If Russian-speaking people in eastern Ukraine asked for Russia's help then Moscow would respond, he said.

"If we see this anarchy beginning in the eastern regions we reserve the right to use all means," he said.

Hundreds of pro-Russian demonstrators have been rallying in Donetsk and other parts of eastern Ukraine, rejecting the new pro-Western leadership in Kiev.

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At the scene

Mark Lowen BBC News, Sevastopol

The rumoured deadline had many on edge. It has has been peaceful overnight, though there were reports of a couple of warning shots fired at Sevastopol airport.

There is an atmosphere of fear and conjecture.

Russian soldiers and local self-defence units are still at key installations, including Ukrainian military bases.

At one base, in Bakhchisaray, a 22-year-old Russian soldier, Vitaly, said they were guarding the base against Ukrainian nationalists. "The people want us here, this is not an occupation," he said.

A Ukrainian soldier there said "it's a Russian provocation. I answer to my government in Kiev - I'm not going anywhere".

At the front gate was a pro-Russian civilian group with blaring music. One of them said they were protecting locals from "fascism".

• Does Russia have a case?
• Military balance of power

Earlier on Tuesday, Mr Putin announced the end of massive Russian military exercises near Ukraine's border and ordered the troops back to barracks.

Ukraine says some 16,000 Russian troops have arrived in Crimea in recent days.

But Mr Putin insisted that pro-Russian "local forces of self-defence" - not Russian troops - were responsible for taking over official buildings in Crimea.

There is international concern about the economic fallout from the crisis. On Monday the rouble plunged to new lows against the dollar and euro, but global markets steadied on Tuesday.

An aide to Mr Putin said that if Washington imposed economic sanctions, Russia could refuse to repay loans to US banks.

Ukraine's economy relies on Russian gas - and on Tuesday the head of Russia's gas monopoly Gazprom, Alexei Miller, said that from April Ukraine would no longer get discounted gas, because it had violated its agreements.

Defending Yanukovych

Referring to the overthrow of Mr Yanukovych, Mr Putin said the ousted leader had agreed to all of the opposition's demands.

He insisted that Mr Yanukovych was still the legitimate president, and accused the West of encouraging the street protests that had ousted him.

There were only three legal means to remove a president, he said: death, personal resignation or impeachment.

Mr Yanukovych fled to Russia, and Mr Putin told the news conference: "I don't think he has a political future."

Russia had helped him for "humanitarian" reasons, he said, "otherwise he'd just have been killed".