Russian Foreign Minister Sergei Lavrov issued the warning in a telephone call to US Secretary of State John Kerry.
It came hours after Russian and Crimean leaders signed a treaty absorbing the peninsula into the Russian Federation following a disputed referendum.
On Wednesday there were reports of an incident at a naval base in Sevastopol.
An Associated Press reporter at the scene said pro-Russian self-defence forces had broken into the building – the headquarters of the Ukrainian navy – and raised the Russian flag.
But the Ukrainian navy told the BBC a group of civilians who said the base was now on Russian territory had gone into the building to persuade the Ukrainian troops to leave.
A spokesman for Russian President Vladimir Putin told the BBC the treaty signed on Tuesday was already in effect, and Crimea was now part of Russia.
The BBC’s Richard Galpin in Moscow says that although it must be approved by Russia’s constitutional court and ratified by parliament, there is no doubt MPs will give their full backing when they vote on Friday.
On Monday, the US and the EU imposed sanctions on several officials from Russia and Ukraine accused of involvement in Moscow’s actions in the Black Sea peninsula.
After the signing of the treaty on Tuesday, the White House said those sanctions would be expanded.
US Vice-President Joe Biden accused Russia of a “land grab”.
After Mr Lavrov spoke to Mr Kerry, the Russian foreign ministry said in a statement: “(Crimea) republic residents made their democratic choice in line with the international law and the UN charter, which Russia accepts and respects.
“The sanctions introduced by the United States and the European Union are unacceptable and will not remain without consequences.”
It did not spell out what those consequences might be.
Mr Kerry later warned that any incursion by Russia into eastern Ukraine would be “as egregious as any step I can think of”.
“I hope we don’t get there,” he added.
On Tuesday, Mr Putin said Western sanctions would be viewed as an act of aggression, and that Moscow would retaliate.
As tension increased, Ukraine’s military said on Tuesday that an officer had been killed in an attack on a base in the Crimean capital Simferopol.
At the same time, pro-Kremlin authorities reported that a member of their own forces had also been killed in the incident.
The government in Kiev said it had authorised its troops to fire in self-defence.
Interim Prime Minister Arseniy Yatsenyuk told an emergency meeting: “The conflict is shifting from a political to a military stage.
“Russian soldiers have started shooting at Ukrainian military servicemen and that is a war crime.”
The BBC’s Mark Lowen in Simferopol says there are fears that further clashes could follow.
In his speech at the Kremlin on Tuesday, Mr Putin told a joint session of Russia’s parliament that Crimea had “always been part of Russia” and in signing the treaty he was righting a “historical injustice”.
He later appeared before crowds in Moscow’s Red Square, telling them: “Crimea and Sevastopol are returning to… their home shores, to their home port, to Russia!”
Ukraine’s interim President Olexander Turchynov said Russia’s actions were reminiscent of Nazi Germany’s takeover of Austria and the Sudetenland.
The Ukrainian crisis began last November after pro-Russia President Viktor Yanukovych ditched an EU deal in favour of stronger ties with Moscow.
He fled Ukraine on 22 February after protests in which more than 80 people were killed.
Pro-Russia armed men then took effective control of Crimea which has been part of Ukraine since 1954 but has a predominantly ethnic Russian population.
The Crimean port city of Sevastopol is home to the Russian Black Sea fleet.