The unrest occurred on Saturday before a late-night meeting in Gaza between Ismail Haniya, the prime minister, and Mahmoud Abbas, the president.
The two men, involved in a power struggle since Hamas defeated Abbas' Fatah Party in legislative elections in January, hoped to iron out their differences, officials said.
Haniyah has complained that Abbas has stripped the government of many of its powers.
Abbas, who seeks a resumption of peace talks with Israel, wants Hamas to soften its hard line against Israel.
Azam al-Ahmed, a Fatah official, said in advance of the meeting that "they are going to discuss every small issue and every big thing, whether financial or security".
"We hope through dialogue we can reach something realistic," he added.
Hamas, sworn to Israel's destruction, has come under intense international pressure to change its ways.
After the cabinet took office in late March, the US and European Union, the two biggest donors to the Palestinian Authority, cut off hundreds of millions of dollars in aid, demanding the Islamist group renounce violence.
Hamas has rejected the calls, despite a financial crunch that has left the treasury broke and unable to pay the salaries of 165,000 government workers for the past two months.
Abbas is to meet with Haniya
late on Saturday
The government is by far the largest employer in the West Bank and Gaza Strip, and many families are scraping by on dwindling savings, loans and handouts.
Teachers at five schools in the West Bank city of Hebron cancelled classes on Saturday to demand their salaries.
While the strike affected only a small number of the city's schools, it marked a turning point.
The Palestinian public has largely backed the government's contention that the crisis is the result of Western hostility to Hamas and so far has heeded calls to remain patient.
"I haven't received a salary for 66 days. Of course I'm not happy with the government," said one teacher.
"I need to live and I need to feed my children."
The teacher, a father of six, asked that his name be withheld, fearing he could lose his job for speaking to the media.
In Nablus, also in the West Bank, hundreds of government workers demonstrated to demand their salaries.
Shaikh Majid Dwikat, a local religious leader, said that "if this government can't function, it has to think carefully about its people and change its political way of thinking".
Most of the participants at the Nablus rally were Fatah supporters, reflecting the growing tensions with Hamas.
The Palestinian population is
heavily dependent on foreign aid
Fatah dominated Palestinian politics for four decades before losing the January parliamentary vote.
About 150 people, mostly women and children, rallied in the Gaza city of Rafah, criticising the government for the growing hardship.
The protesters, banging empty pots with large spoons, urged the government to provide milk for children and medicine for the ill.
Late on Saturday, Russia delivered $10 million in emergency aid to the Palestinians, bypassing the Hamas-led government by sending the money to Abbas' office.
Palestinians have been donating
to help tide over the funds crisis
Abbas immediately distributed the money to a variety of health and education programmes agreed upon with Russia, his office said.
The transactions were handled with the knowledge of Hamas, Abbas' office said.
Palestinian officials said the delivery of the aid could serve as a model for a European proposal to set up a fund, administered by the West, to funnel humanitarian aid to the Palestinians without dealing with Hamas.
The so-called Quartet, which includes the US, EU, Russia and the UN, is expected to discuss the proposal on Tuesday.