* EU maritime mission gains more power to seize weapons

* EU also hopes controlling arms will help Libyan gov't

* Also says moves will help break migrant smuggling gangs

By Robin Emmott

LUXEMBOURG, June 20 (Reuters) - The European Union on Monday gave its naval force in the Mediterranean the authority to search suspicious vessels at sea in a bid to stop arms getting to Islamic State in Libya and to break up gangs smuggling migrants to Europe.

EU foreign ministers acted to boost the effectiveness of the five-frigate "Sophia" mission after winning a U.N. mandate to reinforce an arms embargo on Libya, where Islamic State is strengthening its grip, and limit the near-impunity of the people smugglers.

"We must act, both against those who exploit the migrants, those traffickers who exploit this misery, and against the arms trafficking that benefits Daesh," French Foreign Minister Jean-Marc Ayrault told reporters at a meeting in Luxembourg, referring to Islamic State militants.

European military powers Britain, France and Germany say ending the chaos in Libya that has reigned since the fall of Muammar Gaddafi in 2011 is a crucial part of the EU's moves to end the migrant crisis. NATO ships have also been sent to the Aegean to stem uncontrolled flows to Greece from Turkey.

Although EU ships in the central Mediterranean have picked up around 16,000 migrants at sea in the past year, their limited tasks of surveillance and information-sharing have meant they were not able to destroy weapons, catch traffickers or head off migrants trying to reach Europe by sea from Libya.

At least one smuggler vessel loaded with arms was allowed to pass an EU inspection in the Mediterranean in the past few months for lack of U.N. authority to act, one diplomat said.

Now, the European Union also hopes NATO ships already patrolling in the central Mediterranean could link up with its "Sophia" mission, providing intelligence about smuggling routes.

The United States has said it supports such a move.

"ACCESS TO AMMUNITION"

Gangs, using profits from people smuggling into Europe, control arms networks stretching across Europe into North Africa via the Mediterranean.

Libya U.N. envoy Martin Kobler has told the Security Council that Libya is already awash with arms, with 20 million pieces of weaponry in the North African state of six million people.

By controlling new flows, the West could grant exemptions in the arms embargo to provide weapons to the U.N.-backed unity government in Tripoli and help it assert control in the lawless country.

"Getting control of illegal arms trafficking then gives the international community a lever, because we can consider relaxations in the arms embargo to allow certain groups access to ammunition," said Britain's Foreign Secretary Philip Hammond.

Britain is expected to send another ship to the mission, as well as helicopters and other assets from 24 EU governments.

The EU and NATO say they could operate closer to Libyan shores if requested by the Libyan government, but for now the EU will focus on training the Libyan coast guard in international waters to help combat smugglers. (Reporting by Robin Emmott; Editing by Richard Balmforth)