A third attacker in the massacre of tourists in Tunisia's national museum is on the run, President Beji Caid Essebsi said on Sunday, vowing to track him down.

"Definitely there were three," Essebsi told France's iTele television and Europe 1 radio.

The deadly attack on Tunisia's National Bardo Museum highlights security shortcomings in the birthplace of the Arab Spring which touts itself as regional example of post-revolutionary democracy.

Since Wednesday's assault claimed by the Islamic State group killed 21 people, 20 of them foreign tourists, there has been concern about what the political fallout will be.

Top EU officials said Friday they would visit Tunisia this month to back the fight against a growing Islamist militant threat from north Africa after this week's deadly Tunis museum attack.

European Council President Donald Tusk and EU diplomatic chief Federica Mogherini will travel to the Tunisian capital on March 31 to show solidarity after the attack in which several European tourists were killed.

More than 45,000 Egyptians have fled Libya since jihadists published a video last month showing the beheading of Coptic Christians, most of them Egyptian, an official and state media said Friday.

Hundreds of thousands of Egyptians work in the restive country to the west and send money home to support their families, but their exact number is uncertain because many enter illegally.

EU leaders said they would discuss Friday the attack in Tunis that left many European tourists dead and how unrest in neighboring Libya threatens broader European security.

The Islamic State group claimed responsibility for Wednesday's attack that left 21 people dead, including two Spaniards, a British woman, a Belgian woman, two French, a Pole and an Italian, authorities said.

Tunisia said two gunmen who killed 21 people at its national museum trained at a militant camp in Libya, as the country marked Independence Day in sombre fashion on Friday.

The Islamic State jihadist group has claimed Wednesday's attack on foreign tourists in Tunis, the deadliest since Tunisia's 2011 revolution, which sparked the Arab Spring regional uprisings.

A British tourist was among those killed in the attack on a museum in Tunis, Prime Minister David Cameron said Thursday, vowing to fight against extremists "with everything we have."

"We will not let terrorists undermine democracy," he said in a tweet.

Tunisia has vowed to wage "a merciless war against terrorism" after Wednesday's carnage at its national museum but it has struggled to draw up a strategy to counter the jihadist threat.

Analysts say the attack on the Bardo museum next to the Tunisian parliament in which gunmen killed 21 people, all but one of them foreign tourists, highlighted the need to combine a clear vision with the operational means.

Italy said Thursday it would increase its military presence in the central Mediterranean, describing a deadly attack on a museum in Tunis as fresh evidence of a growing threat from extremist groups.

"Following a worsening of the terrorist threat, dramatically demonstrated by yesterday's events in Tunisia, an increase in our air and naval deployments in the central Mediterranean has become necessary," Defense Minister Roberta Pinotti told the parliamentary defense and foreign affairs committee.

The Islamic State jihadist group claimed responsibility Thursday for an attack on foreign tourists at Tunisia's national museum that killed 21 people, as the security forces swooped on suspects.

The authorities said they had identified the two dead gunmen behind Wednesday's assault, which prompted calls for a show of national unity against extremism in the birthplace of the Arab Spring.