Saudi Arabia has broken up a "major terrorist network" linked to al-Qaida groups in Syria, Iraq and Yemen that was plotting attacks against government installations and foreign interests, authorities in Riyadh said.

The Saudi interior ministry said security forces had arrested 62 suspected members of the group, including three foreigners and 35 Saudi nationals who had previously been detained on terrorist-related allegations and freed.

Members of the organisation have "links with extremist elements in Syria and Yemen," the ministry said. Authorities were still hunting for 44 others.

Major-General Mansour al-Turki, the ministry spokesman, also told reporters in the capital that the Saudi organisation had made direct contact with the Islamic State in Iraq and the Levant (Isis), an al-Qaida linked jihadi group that is fighting the Syrian government and other rebel groups.

The group had been targeting Saudi "government and foreign interests" and had planned "large-scale assassinations", Turki said. The arrests had been facilitated by "suspicious activities on social networks" – which are assumed to be closely monitored by Saudi intelligence.

"Elements of al-Qaida in Yemen were communicating with their counterpart elements in Syria in coordination with a number of misguided [people] at home in various provinces of the kingdom," Turki added.

Saudi security forces also dismantled a factory used to make explosives and electronic detonators and seized about 1 million Saudi riyals (£156,000). The suspects had been involved in smuggling people and weapons across the southern Saudi border.

The announcement comes against a background of growing anxiety in the conservative kingdom about the risk of "blowback" from jihadi groups fighting in Syria, despite enthusiastic Saudi government and private financial and logistical support for the overthrow of President Bashar al-Assad.

Last month, the head of Saudi intelligence, Prince Bandar bin Sultan, resigned after apparently losing an internal argument about security priorities. Prince Mohamed bin Nayef, the interior minister and a possible future candidate for the throne, has been working to discourage Saudis from going to Syria, fearing a repeat of what happened when young Saudi men, including Osama Bin Laden, were authorised to fight the Soviet Union in Afghanistan in the 1980s.

In March, the Saudi interior ministry published a list of "terror" groups, including the al-Nusra Front, which is al-Qaida's official Syrian affiliate, Isis, and Egypt's Muslim Brotherhood. The list also included the little-known Saudi Hezbollah group and Huthi rebels fighting in neighbouring Yemen, both of which may be linked to Iran.

Saudis are now officially banned from "participation in, calling for, or incitement to fighting in conflict zones in other countries" as well as calling for demonstrations or taking part in them.

Saudi Arabia effectively defeated al-Qaida on its own soil after a wave of terrorist attacks between 2003 and 2006. Members of that group went on to merge with Yemeni extremists to form al-Qaida in the Arabian Peninsula (Aqap), which is based in Yemen and seen as one of the network's most formidable affiliates.

Others who were arrested went through much-vaunted official rehabilitation and re-education programmes. General Turki said these programmes could not be 100% effective but insisted that there was no better alternative.