Libya's leader, Muammar Gaddafi, ­yesterday called for a jihad, or holy war, against Switzerland, in an escalation of his vendetta against the country where police once arrested his son.

At a meeting in the city of Benghazi to mark the prophet Muhammad's birthday, Gaddafi described the country as an infidel state that was "destroying" mosques. Last year he urged the UN to abolish Switzerland and divide it between Germany, France and Italy.

"Any Muslim in any part of the world who works with Switzerland is an apostate – is against Muhammad, God and the Qur'an," Gaddafi said.

Swiss voters last November backed a referendum proposal banning the building of minarets. The proposal was put forward by the Swiss People's party, (SVP), the largest party in parliament, which claims minarets are a sign of Islamisation. The move was opposed by the government, which argued that it would harm Switzerland's image, particularly in the Muslim world.

Gaddafi has nursed a grudge against Switzerland since his son Hannibal and daughter-in-law were arrested in Geneva in 2008 for allegedly beating two servants at a luxury hotel. The Gaddafis were released soon afterwards and the charges dropped. But the Libyan leader was so enraged by his son's two-day detention that he shut subsidiaries of Swiss firms in Libya, had two Swiss businessmen arrested, cancelled most flights between the two states and withdrew about $5bn (£3.2bn) from his Swiss bank accounts.

One of the Swiss businessmen has been freed, but the other was forced this week to leave the Swiss embassy in Tripoli, where he had sought refuge, and move to jail to serve a four-month term, in an apparent bid to appease the Libyan leader.

Libya claims the Geneva arrest and the case of the businessmen are not linked.

"Let us fight against Switzerland, Zionism and foreign aggression," said ­Gaddafi, adding that "this is not terrorism", in contrast with the work of al-Qaida, which he called a "kind of crime and a psychological disease". "There is a big difference between terrorism and jihad, which is a right to armed struggle," he said.

"The masses of Muslims must go to all airports in the Islamic world and prevent any Swiss plane landing, to all harbours and prevent any Swiss ships docking, inspect all shops and markets to stop any Swiss goods being sold," Gaddafi said.

Italy warned that Libya may renege on a deal to control the flow of illegal immigrants because of the rift between Gaddafi and Switzerland.

Tripoli has stopped issuing visas to citizens of 25 European states in the Schengen passport-free zone, in retaliation for a decision by Berne to bar entry to some Libyans, including Gaddafi's family.

Italy, which has close business links with Libya, has accused Switzerland of misusing the Schengen agreement and taking EU members "hostage" with the ban, which had forced other states to bar travel by Libyans as well.

Italy's interior minister, Roberto Maroni, said the row put the Schengen zone at risk and could prompt Libya to end co-operation in controlling illegal immigration to the EU.