"France's ambassador returned to Italy on Friday, professing confidence that the two neighbors could deal with disagreements and work through their most serious diplomatic dispute since World War II. 
Italian President Sergio Mattarella received the returning ambassador, the presidential Quirinal Palace in Rome said.
Ambassador Christian Masset gave him a letter from French President Emmanuel Macron inviting Mattarella to France.
"President Mattarella, in expressing thanks, has cordially accepted the invitation," the palace said in a statement.
France recalled Masset last week to protest perceived Italian meddling in French domestic politics, after Italian Deputy Premier Luigi Di Maio met with French yellow vest activists seeking to run for the European Parliament.
"I was very happy to turn the lights back on in Palazzo Farnese," home of the French embassy in Rome, Masset told reporters Friday evening in a frescoed salon of the 16th-century Renaissance palace. "And I want them always to be on."
In response to France's decision, Di Maio, who heads the populist 5-Star Movement, said he was glad France sent the ambassador back to Rome.
"I'll ask him for a meeting," Di Maio told reporters.
Masset for his part welcomed what he perceived as openness by Di Maio to dialogue and the Italian leader's distancing, in remarks on Friday, from any violent elements in the French opposition movement to Macron.
As for relations between Italy and France, which share a border and are major trading partners, Masset said: "We don't deny that there are differences or disagreements on themes, but all can be faced through dialogue and in reciprocal respect" in the interest of both countries.
In remarks in Rome earlier on Friday, Di Maio appeared to want to tamp down speculation the 5-Stars were making alliances with violent elements in the French movement.
"We don't have any intention of dialoguing with that mind-set (of the movement) that speaks of armed struggle or civil war," Di Maio said.
Di Maio has been courting support from fellow populists elsewhere in the European Union with the aim of creating a like-minded faction in the European Parliament after elections this spring.
Adding to the French-Italian tensions, Di Maio's fellow deputy premier, Matteo Salvini, has sharply attacked France lately on migrant policies. Salvini has also demanded France extradite to Italy several Italians who were convicted of domestic terrorism decades ago but who took refuge in France.
Earlier this week, Macron called Mattarella to discuss the removal of Masset. At the time, Mattarella's office said the two presidents" re-affirmed the importance, for each of the two countries, of the French-Italian relationship, which nourishes itself with historic, economic, cultural and exceptional human ties."
Both men further noted that the two countries" have a special responsibility to work in concert for the defense and relaunching of the European Union,"" the Italian presidential office said.