It was the first demonstration allowed by Cuba near the perimeter of the US military enclave where 500 suspected members of al-Qaida and Taliban fighters have been held without trial for more than three years.
Twenty-two Catholic activists of the Witness Against Torture group, including a nun and a priest, have camped out since Monday at a Cuban military checkpoint 8km from the US base, which is as close as Cuba had allowed them to get.
They used a cellular telephone to call the military base, the US Southern Command and the White House to request access to the detainees, but got no reply.
Dana Brown, from Ithaca, New York, said: "We have a Christian president and we live in a country that is based on Christian values. He should let us in to do our mercy work.
"We will continue our vigil and fast until we are allowed into the base to see the prisoners and apologise to them."
The protest coincided with growing international demands from politicians, human-rights organisations and the Red Cross to see the Guantanamo detainees, and accusations they are being treated cruelly.
Washington says they are "unlawful enemy combatants" and not prisoners of war covered by the Geneva Convention. It insists they are being treated humanely, but has refused requests by the Red Cross and others to interview them.
International rights groups have
demanded access to detainees
The American activists defied a US ban on travel to Cuba, and took Cuban authorities by surprise when they flew to the island last week.
Led by Frida Berrigan, daughter of Vietnam War protester Father Philip Berrigan, they marched 80km in four days across eastern Cuba carrying banners that said "Stop the torture," "Free the prisoners" and "Close the naval base".
No man's land
The Cuban military rarely allows civilians, let alone foreigners, near the 28km security perimeter, a no man's land of mines and barbed wire fences surrounding the base the US has held for a century at the entrance to Guantanamo Bay.
Jacqueline Allen, a Catholic worker from Connecticut, said: "We came to Cuba because this is where our government is torturing people in our name".
"We came to Cuba because this is where our government is torturing people in our name"
Catholic worker, from Connecticut, USA
The US government accused the activists of ignoring human-rights abuses in Cuba, where it said 300 dissidents are "languishing" in jails in "horrific conditions" for their political views.
In a statement, the State Department said: "These protesters, as they march through Cuba, are ignoring one of the most oppressive regimes in the world and its systematic and institutionalised violations of human rights that are the hallmark of the 46 years of Castro's dictatorship".