Hundreds of the prisoners have been refusing food since April 17 over conditions for about 6,500 Palestinian inmates.
Speaking to senior members of his Fatah party in Ramallah after meeting President Donald Trump's special representative Jason Greenblatt, Abbas said he had spelt out his position to the envoy who would convey it to the Israelis.
"We have explained in detail to American envoy Jason Greenblatt the issue of the prisoner strike and we have called for American intervention to ensure that the rights of prisoners are protected and their humanitarian demands are granted," he said.
Greenblatt is in Israel and the Palestinian territories to follow up on Trump's visit earlier in the week and to build on his plans for a new Israeli-Palestinian peace initiative, according to Israeli media.
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The hunger strike is being led by prominent Fatah figure Marwan Barghouti, who is serving five life sentences for murders committed during the second Palestinian intifada, or uprising.
Among the strikers' demands are access to telephones, more family visits, improved medical care and an end to punitive solitary confinement.
"From a medical standpoint, we are entering a critical phase," it added, urging the authorities on both sides to find a solution to the standoff.