Separatists have issued a string of demands, including a special status for Corsica in the constitution, greater autonomy and amnesty for those jailed for pro-independence violence.
But Mr Macron’s visit did little to encourage the nationalists their calls will be met.
The island’s assembly chief Jean-Guy Talamoni told France’s Europe 1 radio: “Corsica isn’t just an administrative region [of France].
“If Paris fails to take into account the demands of the absolute majority, then that would mean that democracy does not apply to Corsica and that is simply unacceptable.
“It would be a humiliating blow to Corsicans, and everyone knows that you cannot build anything on humiliation… Corsicans will continue to take to the streets to call on Paris to respect democracy.”
Mr Talamoni is one of the leaders of the nationalist-separatist alliance Pè a Corsica – which holds nearly two-thirds of seats in the regional assembly.
The party wants a special status for Corsica in the constitution and greater autonomy, as well as equal status for the French and Corsican languages and amnesty for militants jailed for pro-independence violence.
Mr Macron has said that he is open to some changes, but has refused several of their demands, including official status for the Corsican language and amnesty for political prisoners, an incredibly thorny issue.
“Corsica, a proud and dignified land, was dirtied by this crime,” Mr Macron said in reference to the murder of Claude Erignac, the island’s prefect who was shot dead by nationalist militants in Ajaccio 20 years ago.
The president added: “[The murder] can’t be justified, can’t be pleaded, can’t be explained… Justice was delivered and will be followed, without complacency, without forgetting, without amnesty.”
Mr Macron’s speech, however, was slammed by a top Corsican lawyer who accused the president of stripping the militants who had been charged with orchestrating Mr Erignac’s murder of their “right of defence”.
Mr Erignac’s said: “The president implied in his speech that some people should not have access to legal support because of the nature of the crime committed and of who the victim was,” lawyer Stéphane Nesa said in a statement on Tuesday.
“The president’s choice of words cannot be interpreted as anything other than a gross violation of the right of defence.
“[His speech] is an unprecedented attack on the fundamental principles recognised by the laws of the Republic.”