Macron's two-day visit to Corsica is being closely watched on the mainland, where some fear that giving the Mediterranean island too much autonomy could fuel a breakaway bid in the future.
The nationalists, who cemented their control of Corsica's regional assembly in December elections, have denied any plans to try to take the territory of 330,000 people out of France -- at least for the time being.
Macron began his visit with a tribute to Claude Erignac, the state's top representative on the island who was assassinated 20 years ago in an attack that shocked the country.
Addressing a ceremony in the city of Ajaccio, Macron said Corsica had been "sullied" by the killing, over which nationalist Yvan Colonna is serving a life sentence, and that there would be "no forgetting and no amnesty".
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He stressed that Corsica, which is economically dependent on the mainland, was part of the "unwavering" French Republic.
He promised, however, to try to give it "the future it aspires to, without giving into demands that would take it out of the Republican fold."
Nationalists have a string of demands, including making Corsican an official language and granting amnesty to Corsicans jailed for
A longtime hotbed of anti-French militancy, the mountainous island has enjoyed a measure of stability since 2014 when the separatist National Liberation Front of Corsica (FLNC) called a ceasefire.
Erignac was gunned down on February 6, 1998 while on his way to a concert with his wife.
The killing was the worst in a nearly four-decade campaign of attacks on the island, mostly targeting state infrastructure.
Tens of thousands of Corsicans took to the streets in protest.
Erignac's widow and two children attended Tuesday's ceremony, as did the leader of the regional government, Gilles Simeoni, who later held talks with Macron.
Macron's meeting with Simeoni and fellow nationalist leader Jean-Guy Talamoni lasted more than two hours but none of them commented afterwards.
Earlier, Talamoni said he would be "dismayed" if Macron "closes the doors" to dialogue. "We are convinced that Mr Macron is a man intelligent enough to understand the situation" and "that what we want to do is in the interests of Corsica and also Paris," he added.
The wife of Colonna, jailed for killing Erignac, stopped Macron in the street late in the afternoon, saying their six-year-old son had not seen his father for a year and a half. "He's not an animal, he's a human being," Stephanie Colonna said.
"That your child can see his father, that people who are detained in our country can see their family, that's one of the things we will ensure," said Macron.
The Corsican question has plagued successive French governments for nearly half a century.
Unlike the separatists in the wealthy Spanish region of Catalonia, who mounted a breakaway bid last year, Corsica's leaders have said they will be content with greater autonomy and a special mention in the constitution.
On Saturday, thousands of nationalists marched to demand "respect for the Corsican people."
Macron had suggested during campaigning for president that he was prepared to go further than his predecessors in recognising the distinct nature of the island.
He will set out his policy in a highly anticipated speech in the northern city of Bastia on Wednesday.