The White House announcement came as US President Barack Obama in an executive order imposed sanctions related to Russia's incursion into Ukraine.
The sanction was also imposed on former Ukrainian President Viktor Yanukovych.
"The US also will seek to hold accountable individuals who use their resources or influence to support or act on behalf of senior Russian government officials," the White House said.
The announcement came shortly after Crimea's parliament today declared the region an independent state after a referendum held yesterday.
Earlier in the day, the European Union announced travel bans and asset freezes on 21 people they have linked to the unrest in Crimea.
EU Foreign Ministers today unveiled travel bans and asset freezes against 13 Russian officials and eight Ukrainian officials from Crimea.
Lithuanian Foreign Minister Linas Linkevicius tweeted that there would be "more EU measures in (a) few days."
The new executive order authorises US Treasury Secretary Jack Lew to work with Secretary of State John Kerry to impose sanctions on "any individual or entity that operates in the Russian arms industry, and any designated individual or entity that acts on behalf of, or that provides material or other support to, any senior Russian government official", it said.
"We stand ready to use these authorities in a direct and targeted fashion as events warrant," it added.
In response to the Russian government's actions contributing to the crisis in Ukraine, this new order lists seven Russian government officials who are being designated for sanctions.
The officials named in the list were Vladislav Surkov, Sergey Glazyev (both aides to President Vladimir Putin), Leonid Slutsky, Andrei Klishas, Valentina Matviyenko, Dmitry Rogozin, and Yelena Mizulina.
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