Gaza protesters call on Palestinian leader to quit power
"Leave!" yelled crowds made up mainly of supporters of Hamas and Mohammed Dahlan, an Abbas rival expelled from the president's Fatah party and who now lives in exile.
They called on the Palestinian Authority to pay the full salaries of public sector employees in Gaza, run by Islamist movement Hamas.
Abbas, 83, has over the course of recent months reduced salaries in the Gaza Strip.
Protesters demanded increased electricity supplies to the enclave, where residents receive power in around eight-hour intervals.
They also demonstrated against Israel's more than decade-long blockade of the Gaza Strip.
Israel claims the blockade is necessary to prevent Hamas, with whom it has fought three wars since 2008, from obtaining weapons or materials that could be used to make them.
Hamas seized control of Gaza in 2007 in a near civil war with Abbas' Fatah.
Multiple reconciliation attempts aimed at restoring the West Bank-based Palestinian Authority to power in Gaza have failed.
Separately in the occupied West Bank on Sunday, around 2,500 people demonstrated in support of Abbas in the city of Hebron.
Abbas was in Egypt's Sharm El-Sheikh on Sunday to attend a European Union-Arab League summit.
He met with Egyptian President Abdel Fattah al-Sisi while there, according to official Palestinian news agency WAFA.
Abbas's term was meant to expire in 2009, but he has remained in office in the absence of elections.