Hundreds of protesters in the West Bank city of Ramallah faced down forces loyal to Abbas, who had banned such rallies earlier in the day.
Abbas's Western-backed Palestinian Authority (PA) has sought to use financial measures to isolate its chief rival Hamas, the terror movement which controls Gaza.
In April 2017, Abbas slashed the salaries of thousands of government workers in Gaza by 30 percent, increasing hardship in the impoverished coastal strip that is home to two million Palestinians.
He has also cut the PA payroll in Gaza by ordering early retirement for nearly a third of its employees.
PA officials said at time that those moves were meant to increase pressure on Hamas to relinquish control of Gaza.
The rivalry between Abbas's Fatah faction and Hamas has simmered for years, and sometimes boiled over into violence since Hamas became a threat to his authority by winning parliamentary elections in 2006 and seizing military control of Gaza in a brief civil war the following year.
Protesting that ordinary Gazans have been caught up in the power struggle between Fatah and Hamas, Palestinian activists have held rallies in the West Bank demanding that Abbas restart the full payment of government salaries and services in Gaza.
Demonstrator Fadi Quran spoke to Reuters as policemen clashed with protesters in the centre or Ramallah. "We came here to demonstrate against the sanctions imposed by President Mahmoud Abbas on Gaza. Sanctions must be lifted," he said.
Protesters held up banners reading, "Gaza unites us. Remove the sanctions."
In an Egyptian-mediated bid to end the rift, Hamas said last year that it would cede control of Gaza to Abbas. But a dispute over how to implement power-sharing has hindered implementation of the agreement.
Abbas' government said on Tuesday that Israel was mainly responsible for Gaza's misery, but it also blamed Hamas.
Israel withdrew its troops and citizens from Gaza in 2005 but maintains tight control of borders, citing security. Egypt also restricts movement in and out of Gaza on its border.