The riots, which began in the south of the Americas' poorest nation and spread to Port-au-Prince, the capital, on Monday, pitted United Nations forces against thousands of hungry Haitians.
 
Hyppolite Melius, another Haitian senator, said Alexis could be forced out if he fails to heed calls that he step aside.
 
Barricades dismantled
 
Rene Preval, the president, promised on Wednesday to boost national food production to reduce dependence on imports, but many protesters demanded immediate action and were disappointed he had not cut taxes on foodstuffs.
 
"Too little, too late. That's the feeling that your proposals have provoked," the senators wrote in their letter to Alexis.
 
"It is obvious that the majority of the people don't believe any more in the capacity of your government to take courageous measures to ease the misery that the population is facing daily."
 
On Thursday the barricades of burning tyres set up by protesters in Port-au-Prince were dismantled and crowds that had surrounded the presidential palace dispersed.
 
Preval had called for calm in a televised address the previous day.
 
The price of rice has doubled in Haiti in less than two months while fuel prices have also risen, a severe problem in a country where most people live on less than $2 a day.
 
"I think that Alexis should resign. We Haitians cannot feed our children. We are living like animals and he is not solving the problems," said Jonas Glezil, a shoemaker.
 
"We don't ask Preval to resign but are waiting to see what he is going to do. If he doesn't act there could be trouble in the future."