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Multiple people were arrested by police, who used tear gas to break up some demonstrations.
In a nationally televised address, President Miguel Díaz-Canel said US trade sanctions had created economic misery on the communist-run island.
Díaz-Canel did not offer the protesters any concessions in his speech.
"The order to combat has been given," he said at the end of his appearance, "Revolutionaries need to be on the streets."
In the city of San Antonio de los Baños, just outside Havana province, hundreds of people defied a heavy police presence to air their complaints.
One resident who did not wish to be identified told CNN that residents had been enduring power outages for a week and that had "detonated" the growing outrage.
Videos uploaded to social media appeared to show other protests in a handful of cities and towns across the island.
In some of the videos, people shouted they "weren't afraid" or that they wanted liberty or access to coronavirus vaccines.
The already struggling Cuban economy has been hit hard as tourism and good imports have dropped steeply during the pandemic.
On Sunday, Cuban health officials reported a record single-day increase for new Covid-19 cases and deaths.