Turkey ready to normalize ties with France: Turkish FM
He said he had had a "very constructive phone conversation" with French counterpart Jean-Yves Le Drian.
"We agreed that we should work on a roadmap to normalise the relations," Cavusoglu told reporters after a meeting with Portuguese Foreign Minister Augusto Santos Silva in Lisbon.
Portugal has just taken over the EU's rotating presidency.
The language was very different to that used by Turkish President Recep Tayyip Erdogan last month.
The spat has risen to new levels in recent months as France has moved to crack down on Islamist extremism after several attacks on its soil.
Erdogan in December said he hoped France would get rid of President Emmanuel Macron as soon as possible.
He added that relations with the 27-nation European Union as a whole would benefit from a "better atmosphere".
At their summit last month the EU leaders decided to draw up a list of Turkish targets for sanctions in response to Ankara's prospecting for gas in Greek and Cypriot waters.