CBS News said that 63 of the 166 men being held at the US-run prison are participating in a 10-week-long hunger strike.
A number of prisoners have joined the strike, which has been ongoing for weeks, in the last few days.
Some sources estimate the protest has grown to as many as 77 inmates, with 25 men joining the cause in the past 72 hours.
Guantanamo spokesman Capt. Robert Durand said 15 men are currently being force-fed liquid nutrients, "to preserve life or prevent serious self-harm," and that two detainees had tried to commit suicide in the past week, CBS said.
The striking detainees, many of whom were captured in Afghanistan and other conflict zones, are angry they have been incarcerated without charge or trial for the past 11 years. Recent reports have cited detainee claims that officials have been searching their Korans and mishandling their holy books.
The strike began on Feb. 6.
Republican Senators John McCain of Arizona and Lindsey Graham of South Carolina, who oppose closing the prison, have suggested that Boston Marathon bombing suspect Dzhokhar Tsarnaev, an American citizen, should be deemed an enemy combatant and sent to Guantanamo.