Ukraine's interior minister has accused Russian naval forces of occupying Sevastopol airport in the autonomous region of Crimea.
Arsen Avakov called their presence an "armed invasion".
But Russia's Black Sea Fleet has denied that Russian servicemen are taking part.
The other main Crimean airport, Simferopol, has also been occupied by armed men. The men are thought to be pro-Russia militia.
The Ukrainian parliament has called on the United Nations Security Council to discuss the crisis in Crimea.
As Ukraine's currency slides, the country's central bank has put a 15,000 hryvnia (1,000 euro; £820) limit on daily bank cash withdrawals.
Meanwhile interim President Olexander Turchynov has dismissed the Armed Forces chief, Yuriy Ilyin.
He was reported to have been admitted to hospital with a heart attack on Thursday.
Mr Ilyin was appointed earlier this month by Viktor Yanukovych, in one of his last acts before being ousted from the Ukraine presidency.
Relations between Russia and Ukraine have been strained since Mr Yanukovych lost power.
These tensions have been particularly evident in Crimea, Ukraine's only Russian-majority region.
The BBC's Bridget Kendall in Moscow says the Crimea is becoming the lynchpin of a struggle between Ukraine's new leaders and those loyal to Russia.
Mr Yanukovych is now in Russia and is preparing to hold a news conference on Friday in the city of Rostov-on-Don, near the Ukrainian border.
He surfaced in Russia on Thursday, asserting that he is still Ukraine's lawful president.
Armed men, said by Mr Avakov to be Russian soldiers, arrived in the Sevastopol military airport near Russia's Black Sea Fleet Base on Friday morning.
The men were patrolling outside, backed up by armoured vehicles, but Ukrainian military and border guards remained inside, Mr Avakov said.
"I consider what has happened to be an armed invasion and occupation in violation of all international agreements and norms," Mr Avakov said on his Facebook page.
Armed men also arrived at Simferopol airport overnight, some carrying Russian flags.
A man called Vladimir told Reuters he was a volunteer helping the group there, though he said he did not know where they came from.
"I'm with the People's Militia of Crimea. We're simple people, volunteers," he said.
"We're here at the airport to maintain order. We'll meet the planes with a nice smile - the airport is working as normal."
After the violent clashes and the ousting of Mr Yanukovych in Kiev, the focus of the Ukraine crisis has now moved to Crimea, which traditionally leans towards Russia.
On Thursday, a group of unidentified armed men entered Crimea's parliament building by force, and hoisted a Russian flag on the roof.
The Crimean parliament later announced it would hold a referendum on expanding the region's autonomy on 25 May.
Russian President Vladimir Putin has urged his government to maintain relations with Kiev and even join Western efforts to bail out its troubled economy.
But he is also giving the Crimean government humanitarian aid.
The US sought assurances from Russia earlier this week, after Russian President Vladimir Putin ordered snap military drills to test the combat readiness of troops near the border with Ukraine.
US Secretary of State John Kerry has called on all sides to "step back and avoid any kind of provocations".
Mr Kerry said he had spoken to his Russian counterpart, Sergei Lavrov, who vowed to respect Ukraine's "territorial integrity".
Crimea - where ethnic Russians are in a majority - was transferred from Russia to Ukraine in 1954.
Ethnic Ukrainians loyal to Kiev and Muslim Tatars - whose animus towards Russia stretches back to Stalin's deportations during World War Two - have formed an alliance to oppose any move back towards Moscow.
Russia, along with the US, UK and France, pledged to uphold the territorial integrity of Ukraine in a memorandum signed in 1994.