Russia's upper house of parliament has approved President Putin's request for Russian forces to be used in Ukraine.
He had asked that Russian forces be used "until the normalisation of the political situation in the country".
Russia's Black Sea Fleet is based in the Ukrainian region of Crimea, where many ethnic Russians live.
Ukraine's acting President Olexander Turchynov said he had put the army on full alert but urged people to remain calm.
In a televised address, he asked Ukrainians to bridge divisions in the country and said they must not fall for provocations.
Prime Minister Arseniy Yatsenyuk, who was standing next to Mr Turchynov, said he was "convinced" Russia would not intervene militarily "as this would be the beginning of war and the end of all relations".
There have been big pro-Russian rallies in several Ukrainian cities outside Crimea:
- In Donetsk, Mr Yanukovych's traditional stronghold, demonstrators from a crowd of some 7,000 tried unsuccessfully to occupy the regional administration building, raising a Russian tricolour on a nearby flag-post
- In Kharkiv, Ukraine's second-biggest city, dozens of people were injured after scuffles between pro- and anti-Russian protesters broke out outside the regional administration building
- In Mariupol, in the south-east, hundreds of protesters carrying Russian flags gathered outside the city council in eastern and southern Ukraine.
Russia's Vladimir Putin submitted the request for troops "in connection with the extraordinary situation in Ukraine and the threat to the lives of Russian citizens", the Kremlin said.
The upper house went into a special session almost immediately after Mr Putin made the request, and swiftly approved it.
Deputy Foreign Minister Grigory Karasin said, however, that this "does not mean that this right will be used quickly" to deploy troops.
The move has alarmed foreign leaders who were quick to express their concern.
UK Prime Minister David Cameron said "everyone must think carefully about their actions and work to lower, not escalate tensions".
UN Secretary General Ban Ki-moon called for "an immediate restoration of calm and direct dialogue", whilst Nato's Anders Fogh Rasmussen tweeted: "Urgent need for de-escalation in Crimea".
US officials said Defence Secretary Chuck Hagel had spoken by telephone to his Russian counterpart Sergei Soigu.
The UN Security Council is holding an emergency session to discuss the crisis, and EU foreign ministers will meet on Monday.
The BBC's Richard Galpin in Moscow says it is potentially significant that Mr Putin's request was for deployment in Ukraine as a whole, and not specifically for flashpoints such as Crimea.
Earlier, the lower house of parliament had urged the president to take whatever measures were necessary to "stabilise" the situation in Crimea.
During the upper house debate, one legislator accused US President Barack Obama of crossing "a red line" with his comments on Friday that there would be costs if Russia intervened militarily in Ukraine.
The upper house has recommended that the Russian ambassador to the US should be recalled, although the decision lies with Mr Putin.
President Putin's request follows days of military activity in Crimea during which unidentified armed men moved in to take over the regional parliament, state television and telecommunications hubs.
Soldiers from Russia's Black Sea Fleet, which is based in Crimea, are reported to be guarding some administrative buildings and military bases.
Amid the closure of airspace over Crimea's regional capital Simferopol on Friday evening, there were unconfirmed reports that Russian planes were flying in thousands of troops.
Ukrainian Defence Minister Ihor Tenyukh said on Saturday there are now an extra 6,000 Russian troops in Crimea, alongside an additional 30 armoured vehicles.
Under the agreement governing the presence of the fleet in Crimea, the Russians must co-ordinate all troop movements outside the fleet's base with the Ukrainian authorities beforehand.
The newly-elected pro-Moscow leader of Crimea, Sergiy Aksyonov, earlier said he had appealed to Mr Putin for help to ensure peace on the peninsula - a request which the Kremlin said it would "not leave unnoticed".
The interim government in Kiev does not recognise Mr Aksyonov and his government, and signed a decree on Saturday that their election at an emergency session of the regional parliament this week was illegal.