"Things may get out of control if the lives of the hunger strikers are not saved," Abbas said on Tuesday.
"We ask the international community to respond effectively to ease the situation, otherwise it will be impossible to control and it will deteriorate across the Palestinian territories.
"These prisoners are on hunger strike in response to the policy of administrative detention and ill-treatment by the occupying authorities," he added in reference to the Israeli regime.
Administrative detention is a sort of imprisonment without trial or charge that allows Israel to incarcerate Palestinians for up to six months. The detention order can be renewed for indefinite periods of time.
Abbas stated that many detainees, particularly Samer Assawi, Jaafar Ezzedine, Ayman Sharawneh, and Tareq Qaadan, are in urgent need of special attention.
He also wrote a letter to UN Secretary General Ban Ki-moon in which he cited the deteriorating health of the hunger strikers and demanded their release.
On Monday, the Free Samer Assawi Campaign said on Twitter that Assawi, who has been on hunger strike for seven months, is dying.
"The longest hunger strike in history and the world doesn't say a thing about it," the campaign tweeted.
The Palestinian prisoners have demanded better prison conditions and urged the Zionist regime to end detention without trial for Palestinians. The striking prisoners have said they will only consume water and salt until their demands are met.
Palestinian prisoners have long complained of the difficulty of securing family visits and the invasive searches visiting relatives have to go through.