(Updates with more quotes, details and context)
PARIS, March 7 (Reuters) - France's foreign minister said on Friday that if a first round of sanctions did not succeed against Russia in the wake of its military intervention in Ukraine, a second could follow, targeting Russian businesses and people close to President Vladimir Putin.
"If there are not very swift results, there will be new measures aimed at those responsible and Russian businesses," Laurent Fabius told France Info radio.
"It could be freezing assets, it could be cancellations, it could be refusing visas," he added, without elaborating.
Fabius called the situation in Ukraine "a serious crisis, maybe one of the most serious since the Cold War".
On Thursday, the local parliament of the Crimea region, where Russian forces have seized control, voted to leave Ukraine and ask to join Russia in a direct challenge to Ukraine's new government in Kiev.
Fabius said any new move by Russia to bring Crimea, which has an ethnic Russian majority, formally under its control could have "grave consequences" for relations between Russia and Europe.
"There will be no more international stability if a region ... because it's solicited by a neighbouring country, can decide to change its borders and attach itself to its neighbour," Fabius added.
Any deterioration of economic ties between Russia and its trading partners could be a "very big blow" to Moscow, Fabius said, adding that any new sanctions could target Putin's inner circle.
An emergency EU summit on Thursday resulted in only minor steps - a suspension of talks with Moscow on visas and a new investment pact - but warned of tougher steps if there was no negotiated solution to the Ukraine crisis.
U.S. President Barack Obama went further, ordering sanctions against figures responsible for the military intervention in Ukraine, including travel bans and a freezing of their assets in the United States, although a U.S. official said Putin was not on the list. (Reporting By Alexandria Sage; Editing by Kevin Liffey)