Lecornu said in his address that "certain elected officials" on the island had brought up the prospect of autonomy.
"According to them, Guadeloupe could better manage itself. They want less equality with mainland France and more freedom of decision for local decision makers," he added.
Paris was also planning on introducing a series of policies for the island, including improving health care, investing in infrastructure and creating more job opportunities for young people.
The economic situation in Guadeloupe is more precarious than in continental France. Some 34.5% of the population live in poverty and 19% of people are unemployed.
Nearby Martinique — also a French Caribbean territory — is one of the better-off overseas territories, but the poverty rate was 29.8% in 2018, according to the National Institute of Statistics.
The French government also announced it would hold off on the vaccine mandate for public sector workers in Guadeloupe and Martinique.
The concession followed protests that turned violent in Guadeloupe, requiring Paris to send extra elite security forces to the Caribbean island.
Protesters in Martinique also threw projectiles at police and journalists on Thursday night. Government spokesperson Gabriel Attal announced "around 150 arrests following the ongoing situation in Guadeloupe and Martinique."
Historic mistrust of the French authorities among Caribbean citizens harks back to the government's handling of a toxic pesticide health crisis. The substance was banned in mainland France in 1990, but its use was allowed to continue on the banana plantations on the two islands for another three years.