Russia has begun issuing Russian passports to residents of Crimea, saying they are now Russian citizens.
Ukraine, meanwhile, has said the Foreign Ministry will start introducing a visa regime for Russians wanting to visit Ukraine.
Russia said it would study Ukraine's move before deciding whether to introduce a visa regime for Ukrainians.
With tensions high on Crimea, pro-Russian forces seized at least one Ukrainian naval base there on March 19 and captured Ukraine's naval chief.
Ukraine's government issued an ultimatum on the evening of the same day, demanding the release of the commander, Admiral Serhiy Haiduk, and other "hostages."
There were no reports of violence as Ukrainian forces evacuated their facilities.
Officials in Ukraine also said they would withdraw from the Russian-led Commonwealth of Independent States (CIS), which groups ex-Soviet countries.
Earlier in the day, Ukrainian authorities resigned from holding the one-year rotating chairmanship of the CIS.
Ukraine, along with Russia and Belarus, was among the founders of the CIS after the 1991 collapse of the Soviet Union.
The announcements on March 19 came one day after Russian President Vladimir Putin and pro-Moscow Crimean leaders signed treaties making Crimea part of Russia.
The annexation has been condemned as illegal by Western states, who have vowed to punish Moscow over the step.
In another development, Ukraine's government said it is drawing up a plan to withdraw its troops from Crimea.
Earlier, the pro-Russian Crimean authorities issued an order to Ukrainian troops to either join Crimean forces or surrender their arms and leave the peninsula.
Announcing that passports had begun to be issued in Crimea, Russia's Federal Migration Service chief Konstantin Romodanovsk also said there are growing signs of what he called "a humanitarian catastrophe in Ukraine."
He did not elaborate, but added that "the number of elderly and children entering Russia has doubled" since early March.
In Washington, NATO chief Anders Fogh Rasmussen sharply criticized Russia's annexation of Crimea.
"We have seen Russia rip up the international rule book, trying to redraw the map of Europe and creating, in just a few weeks, the most serious security crisis since the end of the Cold War," he said. "This sort of behavior goes against international norms and it simply has no place in the 21st century. NATO allies stand with Ukraine. We stand by Ukraine's sovereignty and territorial integrity."
White House spokesman Jay Carney said Russia's seizure of a Ukrainian naval facility created a "dangerous" situation. He said the United States urges Russia to start discussions with Ukrainian officials to ensure the safety of Ukrainian forces in the Crimean peninsula.
Meanwhile, Germany has meanwhile announced it has suspended a military deal with Russia in response to the annexation of Crimea.
The Economy Ministry said the export of a combat simulation center is "not justifiable" in the current situation.
In Britain, Prime Minister David Cameron told parliament that Russia should be cast out of the Group of Eight (G8) leading economic nations.
"I think it's important we move together with our allies and partners and I think we should be discussing whether or not to expel Russia permanently from the G8 if further steps are taken," he said.
United Nations Secretary-General Ban Ki-moon is expected to discuss the crisis when he visits Russia on March 20 for talks with Putin. Ban is then scheduled to travel to Kyiv on March 21 to meet with Ukrainian acting President Oleksandr Turchynov and Prime Minister Arseniy Yatsenyuk.
With reporting by AFP and Reuters