Police in Boden began negotiations during the weekend with the protesters, but the agency's Mikael Ribbenvik said the strikers probably abandoned their action because of a combination of efforts, the Swedish news agency TT reported Monday.
"Two quit yesterday, one in the morning, and the rest during the evening," Ribbenvik said Sunday.
The Afghans, who began their hunger strike in mid-April, were taken to a hospital for medical treatment.
Another group in Holmsund that began a hunger strike at the same time continues to refuse to eat, as well as a group in Gayle in eastern Sweden who began their protests about a week ago.
All of the protesters are seeking residency in Sweden. Several have been rejected; others are waiting for decisions or have decided to seek asylum elsewhere in the European Union.