Relations between Turkey and Europe have been severely strained since several Turkish ministers were blocked from campaigning on the continent for a 'yes' vote in next month's referendum on boosting the powers of President Recep Tayyip Erdogan.
Swiss foreign minister Burkhalter "underscored the validity of Swiss law on Swiss soil, urged Turkey to comply with it," a statement said.
"Freedom of expression is a universal value recognized by Switzerland, which hopes that this freedom will also hold true for Turkish citizens whether they cast their votes in Switzerland or in their own country," it quoted Burkhalter as saying.
Cavusoglu's visit comes after the Swiss government rejected a request from Zurich authorities to cancel a previously planned visit by the minister earlier this month, after the canton's security spokesman warned that a rally he was due to attend could be hit by "heavy demonstrations".
However, the organizers cancelled the event after the hotel they had booked refused to host it.
Swiss police on March 10th also blocked a rally in the northern canton of Aargau supporting a "yes" vote in the referendum.
Ankara has said such behaviour was reminiscent of Nazi Germany, and Erdogan warned on Wednesday that Europeans risk being unsafe on the world's streets if they did not modify their behaviour.
On April 16th, Turks will decide whether to approve constitutional changes that would axe the role of prime minister and could see Erdogan in power until 2029.
While the government argues it is necessary for stability, critics claim it will lead to one-man rule.
Burkhalter expressed concern about a crackdown in Turkey following a failed July 15th coup that the government has blamed on US-based Islamic preacher Fethullah Gulen.
Burkhalter expressed "concern about the large number of dismissals and arrests in Turkey, and underscored that the declaration of a state of emergency does not exempt Turkey from its international human rights obligations," the Swiss foreign ministry said.
Following the putsch, Ankara launched an unprecedented purge of alleged Gulen supporters, with some 43,000 people jailed and awaiting, or on, trial and suspended or sacked about 100,000. Many of them are teachers, police, magistrates or journalists.