The head of the FIS, Markus Seiler, took a calmer stance but spoke of an “elevated” threat, reported Le Temps.
In a statement to release its 2017 situation report, the FIS said the challenges it faced “are becoming increasingly complex”, in part because of the “extraordinary pressure” on Europe “due to a variety of crisis situations”.
These crises have been aggravated in the past year by Brexit, the election of US President Donald Trump and the recent political reform in Turkey, it said.
“This has contributed further to the erosion of old certainties, whose place is being taken by fundamental uncertainty and reduced levels of predictability,” it said.
The “extraordinary pressure” on Europe is “not without consequences” for Swiss strategy, it added.
Contrary to Parmelin's tone during the press conference the FIS said an armed attack on Switzerland “remains unlikely” but that it was undeniable that Europe was becoming more polarized and more heavily militarized.
The terror threat in Switzerland “remains heightened”, it added, principally due to the threat from Isis and the activities of isolated individuals inspired by the terror group.
Just under 500 internet users are on the radar of the FIS for visiting pages related to radical Islam or posting comments in support of jihadists, they said.
Of those, 90 are considered a security risk.
However the number of people leaving Switzerland to join jihad groups has gone down, they said.
Switzerland hasn't recorded a departure for a conflict zone since August 2016.
Since 2001 there have been 88 cases recorded in total, with 14 of those returning to Switzerland where some were convicted.
Violence related to political extremism, cyber attacks and espionage are among the other threats to Swiss security, said the organization.
However Parmelin and Seiler refused to address questions from the media on last week's revelations of a Swiss spy arrested in Germany.
“I cannot, nor do I want to, interfere in a current investigation in a country that is a friend and neighbour,” said Parmelin.