After more than six weeks of protests over the high cost of living on the French Caribbean island of Martinique, the local prefecture has signed a deal to cut soaring food prices.

Jean-Christophe Bouvier, France’s prefect in Martinique, said the deal with a number of groups including importers and distributors would mean a 20% average cut in prices for 6,000 key, imported products.

Martinique has been rocked by protests that have left four people dead in clashes and shops and businesses set alight or looted. Authorities in the French territory have extended an overnight curfew to next week.

However, the deal to cut food prices has been rejected by the group behind the protests.

Food costs are about 40% more in Martinique than in mainland France and the Rally for the Protection of Afro-Caribbean Peoples and Resources (RPPRAC) is demanding that prices on the island are no higher than the mainland.

The RPPRAC says the agreement should cover 40,000 products, not just 6,000, and leader Rodrigue Petitot said it should be across the board rather than limited to 54 types of food.

“We’ll keep fighting until we get our way,” Petitot told AFP news agency.

In a communiqué after a seventh round of negotiations on Wednesday night, the French prefect said the agreement reached would result in five significant measures “for a structural reduction in purchase costs… as well as a firm and mandatory commitment by big distributors to cut significantly their margins on the sale of products”.

About 80% of food is imported from mainland France, so the 360,000 people who live in Martinique have to pay about €7.80 (£6.50) for a 250g packet of branded ground coffee that might cost €3.50 elsewhere. Butter can cost as much as €8.50 and households spend as much as 17% of their income on meat alone.

And it is not just food, where the price gap between France and Martinique has widened significantly in recent years. Phone and internet costs are a third higher, too.

Part of the problem is an old 9% import tax known as octroi de mer (dock dues) dating back to the 17th Century. Another is the large number of intermediaries involved in bringing products to the shops.

“It’s not right for a couple with a child to have to spend €250 on groceries every 10 days for basic food items,” another leader of the protest movement told French media.

Unrest in Martinique broke out on 1 September, prompting protests and roadblocks and a curfew in the capital Fort-de-France.

Riot police were sent to the island later in September, the first such intervention involving a mainland security force since 1959.

Earlier this month a number of police offers were wounded in clashes and a man was fatally wounded by gunfire during the looting of a shopping centre.