EU foreign ministers are due to discuss further sanctions against Russia after a Moscow-backed referendum in Crimea backed a split from Ukraine.
Election officials in Crimea, where pro-Russian forces are in control, say 97% of voters backed joining Russia.
The government in Kiev described the vote as a "circus performance" and said it would not recognise the result.
The EU and US say the referendum was illegal, but Russia says it was consistent with international law.
US President Barack Obama has warned Moscow that Washington is also ready to impose "costs" over its actions in Ukraine.
As polls closed on Sunday night, the White House said the international community "will not recognize the results of a poll administered under threats of violence", describing Russia's actions as "dangerous and destabilizing".
The new authorities in Kiev say Russian troops moved in to Crimea after Ukraine's pro-Moscow president, Viktor Yanukovych, was ousted following months of street protests.
The Kremlin has officially denied deploying its troops in Crimea, describing the armed men without insignia as "Crimea's self-defence forces".
Crimean leaders are expected to formally apply to the Kremlin on Monday to join Russia.
The Russian parliament had been expected to wait until Friday to begin debating the relevant legislation. But the BBC's Richard Galpin in Moscow says it is now believed the process of absorbing Crimea could take place under existing laws.
Whatever the procedure is, the indications so far are that it will happen soon, says our correspondent.
Speaking in Brussels, EU foreign policy chief Catherine Ashton said the "so-called referendum" was "illegal under the constitution of Ukraine and under international law".
"I call upon Russia yet again to meet with Ukrainian leaders and to start a dialogue with them, and to try to move to de-escalation, please, as quickly as possible. We've seen no evidence of that," she told reporters.
She said the EU "can't simply sit back and say this situation can be allowed to happen", but that ministers needed to think carefully about what their response should be.
EU foreign ministers from the 28 EU countries, meeting in Brussels, are considering a visa ban and an asset freeze against a number of Russian officials.
The bloc has already suspended talks on an economic pact with Russia and an easing of visa restrictions.
The ministers will now be toughening the measures by discussing a list of names of those who could be subject to an asset freeze and a visa ban.
However, the question remains whether the target should just be the list of people related to the takeover in Crimea or the inner circle around Russian President Vladimir Putin, the BBC's Europe editor Gavin Hewitt says.
If an asset freeze and visa ban does not rattle Moscow or Russia makes further military moves into eastern Ukraine, he adds, the EU has already warned of moving to another stage which would involve economic sanctions.
Earlier, the EU said in a statement that the vote was "illegal and illegitimate and its outcome will not be recognised".
Crimean voters had been asked whether they wanted to join Russia, or have greater autonomy within Ukraine. There was no option for those who wanted the constitutional arrangements to remain unchanged.
On Sunday night, thousands of Crimeans began to celebrate as news of a landslide pro-Moscow result emerged.
Sergei Aksyonov, Crimea's pro-Moscow leader installed last month after the Russian takeover, appeared on stage in Crimea's regional capital, Simferopol.
Backed by the Russian national anthem, Russian flags, and the personnel of Russia's Black Sea fleet, he told supporters that Crimea was "going home".
On Monday morning, the chairman of the regional election commission, Mikhail Malyshev said complete initial results showed voters were 96.77% in favour of joining Russia.
Some 58% of people in Crimea are ethnic Russian, with the rest made up of Ukrainians and Tatars.
Most of the Tatars that the BBC spoke to said they had boycotted the vote, and felt that life under the Kremlin would be worse.
The Tatars were deported to Central Asia by Soviet dictator Joseph Stalin in 1944. They were only able to return with the fall of the Soviet Union and many want to remain in Ukraine.