With both countries at the frontline of the refugee-migrant crisis, proposals to stem the influx to Europe were at the top of the agenda during their meeting.
European Union leaders have devised a plan involving largely lawless Libya to try to shut down the smuggling of hundreds of thousands of refugees/ migrants from North Africa across the Mediterranean Sea to Europe.
Though they disagree on details, Berlin, Paris and many of the 17 other states that use the euro currency are keen to bind the eurozone closer together after years of crisis in which investors have doubted the currency's survival.
Pope Francis seized control of the Knights of Malta, and action that amounts to one sovereign country annexing another, if on a very small scale.
Muscat warned that the 2015 refugee crisis had caught Europe off guard and that the EU must reach a deal with north African countries before next spring
On Sunday Malta took over the six-month rotating presidency over the European Union from Slovakia that chaired the presidency in the second half of 2016.
Hijackers diverted a Libyan plane carrying 118 people to the Mediterranean island of Malta on Friday and threatened to blow it up with hand grenades, officials said. Tense negotiations ensued and within a few hours all people were allowed to leave the plane, the prime minister said.
Malta is set to take over the Presidency of the European Council in January for the first time since joining the EU in 2004.
A small aircraft conducting a surveillance mission over the Mediterranean for France's Defense Ministry has crashed in Malta, killing all five people on board.