Kerry phoned Abbas to discuss reaching a truce in Gaza based on the Egyptian ceasefire initiative, Xinhua reported.
Late on Tuesday, Abbas said that the Israeli offensive on Gaza is meant to undermine the Palestinian national unity and it was time for everyone "to raise their voices against the Israeli offensive".
Abbas also said that in the last few days, he visited Egypt, Turkey and Qatar and met with Egyptian President Abdul Fattah al-Sisi and leaders of Islamic Hamas movement and Islamic jihad movement, trying to end the bloodshed in the Gaza Strip.
He also pledged to sue Israeli leaders who "committed crimes against the Palestinian people," saying "such crimes cannot pass without punishment."
The Palestine Liberation Organisation's (PLO) executive committee Tuesday night called for an emergency meeting in Cairo of the temporary leadership framework comprising Hamas and Islamic jihad movement.
Abbas: Time for everyone "to raise their voices against the Israeli offensive"
In a statement after a meeting chaired by Abbas, the Palestinian leadership said that it would work hard at all levels to reach a ceasefire deal and unify all Palestinian factions under the PLO.
It also called for massive demonstrations in support of Gaza and its resistance against "the crimes" of the Israeli army.
So far, efforts to mediate a truce in the Gaza Strip have failed.
Earlier Wednesday, UN Secretary General Ban Ki-moon, who is on a visit to Ramallah and Israel, urged both the sides to end fighting and start negotiation for a ceasefire.
Since Israel launched Operation Protective Edge in the Gaza Strip July 8, a total of 631 Palestinians have been killed and 3,750 injured.
Israel has lost one civilian and 28 soldiers.