On a visit to Baku, Burkhalter — who is also chairman of the Organization for Security and Co-operation in Europe (OSCE) — "called on the sides to strictly adhere to the ceasefire agreement" and increase efforts for the conflict's peaceful settlement, the OSCE said in a statement.
Burkhalter backed a proposal for a meeting in Paris between the Armenian and Azerbaijani presidents that "should mark the beginning of a new phase in peace talks," he was quoted as saying by Azerbaijan's state news agency, Azertag.
In Baku, the Swiss president was beginning a three-day visit to the South Caucasus which will see him holding high-level talks in Georgia on Tuesday and Armenia Wednesday.
There has been an increase in violence in recent months along the Azerbaijan-Armenia border and at the Karabakh frontline, with both sides regularly accusing the other of tit-for-tat raids.
Armenia-backed separatists seized Nagorny Karabakh from Azerbaijan in a 1990s war that killed 30,000 people. Despite years of negotiations since a 1994 ceasefire, the two sides have yet to sign a peace deal.
Azerbaijan has threatened to take back the disputed region by force if negotiations do not yield results, while Armenia has vowed to retaliate against any military action.
The Karabakh peace talks are mediated by the so-called OSCE Minsk Group co-chaired by France, Russia, and the United States.