The Special Coordinator also expressed concern for the ongoing hunger strike by Palestinian detainees protesting against their conditions in Israeli jails, which, on the eve of Ramadan, has now entered its 40th day.
The prisoners were fighting for better prison conditions; reinstating a second monthly family visit was one of the concessions the Israel Prison Service offered.
Israelis insist the deal was reached not with prisoners' representative but with the Palestinian Authority and the International Committee of the Red Cross (ICRC). They first tried to portray it as a publicity stunt by the charismatic Palestinian leader, Marwan Barghouti, who is leading the prisoners' hunger strike. It is still unclear whether American intervention brought an end to the strike.
Palestinian protesters argue with Israeli soldiers during clashes in the West Bank town of Beita, May 26, 2017.
In particular, the prisoners demanded ending solitary confinement and detention without trial and the right for more family visits.
"The move effectively reinstated the number of family visits that were traditionally provided to Palestinian prisoners, before the ICRC reduced the number of visits they facilitated past year from two to one visit a month, sparking protests across the Palestinian territory", according to Ma'an.More news: IAS officer drowns while trying to save female colleague in Delhi
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Israel's public security minister, Gilad Erdan, alleged that the hunger strike was motivated by a power struggle in Mr Abbas's Fatah movement. "There is a perception this is a victory for the prisoners, and for Marwan [Barghouti], because he embarked on a strike the Palestinian Authority wasn't that excited about".
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.
The hunger strikers, who began their protest on 17 April, ceased the strike just hours before the holy month of Ramadan, when Muslims fast from sunrise to sunset.
Speaking to Al Jazeera from Ramallah, Majed Bamya, who oversees the prisoner files for the Palestinian foreign ministry, said the outcome of the hunger strike was a success. One of the demands of the prisoners, that there should be an additional visiting day for family members, has been accepted by the Israel Prison Service. He urged the worldwide community to support the prisoners and demanded that Israel respect their rights and human dignity. "Right up to 8 am on Friday, the Israel Prisons Service insisted that no negotiations were possible", Fares told AFP.
After 40 days in, the prisoner's health was deteriorating rapidly, with 182 striking political prisoners having been hospitalized.