The Bank of Palestine said in a statement on Sunday that government employees who held accounts at its branches and earned 1,500 shekels a month ($325) or less could start withdrawing their money from automated teller machines (ATMs).
Mohammed al-Qilani, a policeman, was able to withdraw his salary from a Bank of Palestine ATM in the Gaza Strip on Sunday night.
"I did not believe that the salary would ever be paid again," he said. "I don't believe it even now."
The Palestinian Authority's 165,000 workers have gone without salaries for three months since the Islamic resistance group Hamas took power, prompting Israel and Western countries to cut off aid and other transfers to the administration.
Israel, the United States and the EU regard Hamas as a terrorist organisation. That has also discouraged local, regional and international banks from doing any business with the new government.
The initiative by the Bank of Palestine came after other local banks, in the wake of threats from militants, agreed to pay out of their own funds thousands of other government workers.
The banks said they would provide free loans, covering one month's salary, to the Palestinian government's lowest-paid employees.
By dealing directly with the employees, those banks sidestep the threat of international sanctions against financial institutions that deal with Hamas.