Interior Minister Arsen Avakov said Russian naval forces had taken over a military airport near the port of Sevastopol, where the Russian Black Sea fleet has a base, and other Russian forces had taken over Simferopol international airport.
However, amid the confusion one man who said he was helping the group at Simferopol airport described them as simple people from the "People's Militia of Crimea".
Mr Avakov said tension was rising on the Black Sea peninsula, the only Ukrainian region that has an ethnic Russian majority and the last major bastion of resistance to the overthrow of Viktor Yanukovich as president almost a week go.
"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, describing it as a "provocation" and calling for talks.
Mr Yanukovich is expected to appear before reporters in the Russian city of Rostov-on-Don later on Friday, although President Vladimir Putin has not said whether Moscow will harbour the former leader who is on the run and wanted for mass murder.
The United States has told Russia to demonstrate in the next few days that it is sincere about a promise not to intervene in Ukraine, saying using force would be a grave mistake.
"We believe that everybody now needs to take a step back and avoid any kind of provocations," US Secretary of State John Kerry told a joint news conference with German Foreign Minister Frank-Walter Steinmeier. "We want to see in the next days ahead that the choices Russia makes conform to this affirmation we received today."
The Kremlin said Putin had ordered his government to continue talks with Ukraine on economic and trade relations and to consult foreign partners including the International Monetary Fund on financial aid.
It also said Mr Putin ordered the government to consider a request from Crimea for humanitarian aid but made no direct reference to the latest events.
Mr Yanukovich provoked protests in Ukraine in November by backing out of plans to sign landmark deals with the European Union and instead saying Kiev would seek closer economic and trade ties with its former Soviet master Russia.
In December, Mr Putin promised Mr Yanukovich a $15-billion bailout, but Russia has put the deal on hold after releasing an initial instalment, saying it wants more clarity about the new government and its policies.Armed forces in crimea
Kiev's new rulers have said any movement by Russian forces beyond the Black Sea fleet base in Sevastopol would be tantamount to aggression.
But it faces a major challenge in Crimea which was Russian territory until it was transferred to Ukraine in 1954, during the Soviet era. Separatism there has often flared up at times of tension between Moscow and Kiev.
Unidentified gunmen seized the Crimean parliament and raised a Russian flag on Thursday. The gunmen issued no demands and police were casually guarding the building.
Armed men took control of Simferopol airport overnight and were patrolling its grounds on Friday morning.
A Reuters eyewitness at the scene said the men, dressed in full battle gear and carrying assault rifles and machine guns, were moving freely in an out of the control tower.
A man called Vladimir, who said he was a volunteer helping the group, said: "I'm with the People's Militia of Crimea. We're simple people, volunteers ... We're here at the airport to maintain order. We'll meet the planes with a nice smile - the airport is working as normal."
The Belbek military airport near Sevastopol was taken over by what Mr Avakov said were military units of the Russian fleet and armed men in camouflage were guarding the perimeter fence.
One of the men was quoted as saying the aim was to prevent Mr Avakov flying to Crimea.
"Tension is rising," Mr Avakov said. "While we don't have direct military clashes, diplomats should talk."Sovereignty call
The regional parliament in Crimea managed to hold a session inside the building on Thursday despite the siege, where it voted to stage a referendum on "sovereignty" for Crimea.
Russia's flag still flew from its roof and lights were on in the windows of its top floor. It was not clear whether the armed men were still inside.
Oleksander Turchinov, Ukraine's acting president, warned Russia on Thursday not to move personnel beyond areas permitted by treaty for those using its naval base.
"Any military movements, the more so if they are with weapons, beyond the boundaries of this territory will be seen by us as military aggression," he said.
Russia has repeatedly declared it will defend the interests of its citizens in Ukraine, and announced war games on Wednesday near the border, involving 150,000 troops on high alert. Mr Kerry said Mr Lavrov told him the exercises had been pre-planned.
Although Moscow says it will not intervene by force, its rhetoric since the removal of its ally Yanukovich has echoed the run-up to its invasion of Georgia in 2008, when it sent its troops to protect two self-declared independent regions and then recognised them as independent states.
Witness accounts suggest those who captured the Crimean parliament building in the early hours of Thursday were pro-Russian gunmen of some kind.