On Thursday the Swiss upper house of parliament backed a motion by Liberal-Radical Damian Müller in which he asked the Swiss government to examine the problem, reported news agencies.
According to the text of Müller's motion, some migrants are refused asylum but then manage to avoid being deported, including some who are criminal offenders or may have jihadist sympathies and therefore pose a terror threat.
The Swiss government should find ways to improve current deportation rates and ensure that potentially dangerous people whose deportation is delayed are sufficiently monitored, he said.
The report should also examine whether the costs for this should be borne by the federal government rather than the cantons.
Addressing the issue, justice minister Simonetta Sommaruga said there was no “recipe” for combatting terrorism and that just because someone is refused asylum doesn't mean they are a terrorist.
But the Council of States supported Müller's request.
It will be addressed by the Federal Council as part of a report on police measures related to the fight against terror.