Ukraine has ordered a full military mobilisation in response to Russia's build-up of its forces in Crimea.
Prime Minister Arseniy Yatsenyuk said Ukraine was "on the brink of disaster".
In Crimea, Ukrainian soldiers faced off with Russian soldiers surrounding their bases while the Russian army is said to be digging trenches on the border with mainland Ukraine.
US Secretary of State John Kerry has warned Russia could be ejected from the Group of Eight developed nations.
Russian President Vladimir Putin, he said, was "not going to have a Sochi G8, he may not even remain in the G8 if this continues," referring to a planned summit in Russia in June.
"He may find himself with asset freezes, on Russian business. American business may pull back, there may be a further tumble of the rouble.
"You just don't in the 21st Century behave in 19th Century fashion by invading another country on completely trumped-up pretext," Mr Kerry told the CBS program Face the Nation.
The UK has joined the US, France and Canada in suspending preparations for the Sochi summit.
Nato is conducting emergency talks, saying Russia's actions threaten "peace and security in Europe".
US President Barack Obama called Russian troop deployments a "violation of Ukrainian sovereignty".
Russian soldiers continue to occupy key sites on the Crimean peninsula, including airports and communications hubs, although there has been no actual violence and they have been openly welcomed by some sections of the population.
In the east Ukrainian city of Donetsk, apparent members of the disbanded elite police riot unit Berkut appeared in full uniform at a pro-Russian rally.
In Moscow, police detained dozens of people at anti-war rallies outside the Russian defence ministry and other places in the city centre, while elsewhere in the city a pro-Putin march was held.
Ukrainian national security officials announced several other measures on Sunday
- The armed forces would to be put on "full combat readiness"
- Reserves to be mobilised and trained
- Foreign minister to seek help from US and UK leaders in guaranteeing its security
- Emergency headquarters to be set up
- Security to be boosted at key sites, including nuclear plants
- Airspace to be closed to all non-civilian aircraft
Meanwhile, Ukraine withdrew coast guard vessels from two ports in Crimea and moved them to other bases in the Black Sea and Sea of Azov.
A Ukrainian army base was surrounded by Russian troops at Perevalnoye, south of the Crimean regional capital Simferopol. An Orthodox priest has arrived in an attempt to mediate.
In Sevastopol, Ukrainian naval officers found their headquarters occupied by Russian troops and were unable to go to work.
Admiral Yuriy Ilyn, who was until recently commander of the Ukrainian navy and served briefly as head of Ukraine's armed forces under ousted President Viktor Yanukovych, told the BBC's Christian Fraser at the scene that the armed forces were "hostages of the situation".
In the eastern port city of Feodosia, a group of about 100 Ukrainian marines were also blockaded into their base by armed men demanding they pledge loyalty to the region's new pro-Russian authorities.
In the north of Crimea, at Armyansk on the Isthmus of Perekop, the BBC saw what appeared to be Russian soldiers digging trenches. The isthmus is strategically vital as it joins Crimea to the rest of Ukraine.
Russian ground troops have been active in Crimea - home to Russia's Black Sea Fleet - for the past few days.
On Saturday the newly elected pro-Moscow leader of Crimea, Sergiy Aksyonov, appealed to Mr Putin for help to ensure peace on the peninsula.
The interim government in Kiev does not recognise Mr Aksyonov and his government.
Late on Saturday, Mr Obama held a 90-minute telephone conversation with Mr Putin and urged him to pull forces back to bases in Crimea.
Mr Putin said Moscow reserved the right to protect its interests and those of Russian speakers in Ukraine.
President Putin submitted his request for troops to the Russian parliament on Saturday "in connection with the extraordinary situation in Ukraine and the threat to the lives of Russian citizens", the Kremlin said.
Mr Obama, the White House said, told Mr Putin that the appropriate way to address any concerns was "peacefully through direct engagement" with the Ukrainian government and international mediating bodies.