Those who have surrendered also swore allegiance to the region's pro-Russia government, Prime Minister Sergei Aksyonov said during a news conference.
In Kiev, however, the Ukrainian Defense Ministry said in a statement the information coming from Crimea was "false."
"All the Ukrainian military units, formations, and warships stay in their permanent locations. Ukraine's military controls the territories of their military posts," the statement said.
The Times said it wasn't possible independently to verify claims made by Aksyonov, who did not say all military units in the region were aligned with his administration.
Aksyonov also said local officials were working to speed up setting up a referendum seeking independence from Ukraine.
In Kiev, Secretary of State John Kerry pledged U.S. support to Ukraine's elected government during a visit Tuesday to the Ukrainian capital.
Kerry spoke of how moving it was to drive and walk through the streets where Ukrainians risked their lives and in some cases died to protest ousted President Viktor Yanukovych's actions.
"The United States will stand by the Ukrainian people as they build the strong, sovereign and democratic country that they deserve and that their countrymen and women just so recently gave their lives in extraordinarily courageous acts in order to ensure for the future," he said. "We must all step up and answer their call."
Kerry also reiterated a promise of financial support. Earlier, Treasury Secretary Jack Lew announced the United States will provide $1 billion in loan guarantees and technical expertise to Ukraine.
Kerry met with Ukraine's interim government led by Oleksandr Turchinov as president and Arseniy Yatseniuk as prime minister.
"Specifically, the U.S. administration is working with Congress and the government of Ukraine to provide $1 billion in loan guarantees, the proceeds of which will be aimed at protecting the most vulnerable Ukrainian households from the impact of the needed economic adjustment," Lew said in a statement.
"The United States is also moving quickly to deploy a range of other financing and technical expertise, utilizing a whole-of-government approach to support Ukraine," Lew said. "The departments of Commerce, Justice, Energy, State, Treasury, Federal Bureau of Investigation, and the U.S. Agency for International Development are all preparing to deploy rapid assistance."
He said the Treasury Department was ready to send experienced technical advisers to help the Ukrainian financial authorities "manage immediate market pressures and support Ukraine as it negotiates with the IMF [International Monetary Fund]."
As part of an international effort to support Ukraine's new government, the United States developed a package of bilateral assistance focused on four areas: implementing critical economic reforms and cushioning their impact on vulnerable Ukrainians; conducting free, fair and inclusive elections, with robust involvement by a strong and independent civil society and media; combating corruption and recovering stolen assets; and withstanding politically motivated trade actions by Russia, which has deployed thousands of troops to pro-Russia Crimea, claiming pro-Moscow citizens and Russian-language speakers are in danger from the Ukrainian government.
Russian leaders maintain it is their right and obligation to protect Russian citizens and pro-Russian people in Ukraine where Yanukovych was ousted two weeks ago, fled Kiev and took refuge in Russia. There have been no verifiable reports of violence against Russians in Ukraine.
About 13,000 Russian troops have been deployed to Crimea during the past week, a former senior Russian fleet officer based in Sevastopol told the Kiev Post.
President Obama, speaking to the news media after discussing his proposed budget, said some of the coverage of Ukraine suggested Russia has been "clever strategically."
"I actually think that this is not been a sign of -- of strength, but rather, is a reflection that countries near Russia have deep concerns and suspicions about this kind of meddling, and if anything, it will push many countries further away from Russia," he said.
Russian military forces also were posted in Rostov and Voronezh regions inside Russia not far from Ukraine's border, Ukraine's Foreign Minister Andriy Deshchytsia said.
Russian President Vladimir Putin said he ordered Russian Foreign Minister Sergei Lavrov to work with the German foreign minister on sending an independent, international team to Kiev to investigate events in Ukraine, Interfax-Ukraine reported.
"We have specially trained people who should consider this issue and discuss it with our German colleagues," Putin said during a news conference. "It's generally possible. I have given an appropriate order to our foreign minister, who should meet or is already meeting with the German foreign minister. They will discuss this issue."