House Budget Committee Chairman Paul Ryan called on the Obama administration to hit Russian oligarchs with sanctions in response to Russia's military occupation of Ukraine's Crimea region.

"There are vulnerabilities within Russia that [Russian President Vladimir Putin] has politically that can be exploited," the Wisconsin Republican told CBS's "Face the Nation" on Sunday. "I think we should consider targeting some of the oligarchs around him that are his enablers and he is their enablers."

Ryan suggested imposing travel bans and economic sanctions against Putin's wealthy domestic allies, including targeting overseas holdings "that are illicitly gained through this kleptocracy of the Russian economy."

Ryan also urged the Obama administration to expand natural gas exports to Europe to help the continent become less dependent on Russian gas and oil -- a significant part of Russia's economy.

"We are a nation with vast energy reserves and potential, but with a government that is seen as hostile toward developing those energy reserves, let alone exporting those energy reserves," Ryan said.

"If our government changed its tune on that, if we told Europe we are going to green-light these languishing [natural gas] permit applications for exporting … to Europe, that could do a lot to send the signals that we are intent on loosening Russian's grip on its energy to Europe and that we're going to be a reliable ally to loosen their grip."

He said the House will move forward on legislation to expedite the permitting process for U.S. natural gas exports to Europe.