Izzat al-Rashiq, a member of Hamas, said: "They [the Saudis] affirmed that political and financial aid to the Palestinian Authority and Palestinian people would continue.
"We did not go into numbers, but they promised excellent support."
He was speaking on Saturday after the delegation met Prince Saud al-Faisal, the country's foreign minister, on Friday night.
Hamas leaders are in Saudi Arabia, the world's biggest oil exporter and birthplace of Islam, on a tour of Arab and other countries seeking support after their surprise victory in parliamentary elections in January.
The United States and the European Union have threatened to stop funding the Palestinian Authority unless Hamas, which is gearing up to form a government, gives up its armed struggle against Israel and recognises the Jewish state.
Biggest financial backer
Prince Saud had publicly rejected
a US call to isolate Hamas
Al-Rashiq declined to say whether Riyadh had promised to increase funding to fill gaps caused by Western countries.
Saudi officials were not immediately available for comment.
Saudi Arabia is largely seen as the biggest financial backer of the Palestinian Authority. Saudi citizens and charitable foundations donate about $150 million each year to support social and economic projects in the Palestinian territories.
On Saturday, the Palestinian delegation held separate meetings with Prince Saud and Prince Muqrin bin Abdul-Aziz, the Saudi intelligence chief, the state news agency SPA reported without giving details.
Prince Saud had publicly rejected a US call to isolate Hamas during a visit by US Secretary of State Condoleezza Rice last month.
"We believe the Saudi position ... will be extremely important in breaking the embargo that America and Israel want to impose on our people," al-Rashiq said.
"It is completely unreasonable to cut off an entire people."
Saudi snub to US
About three million Palestinians under Israeli control since the 1967 Middle East war want an independent state. But Hamas has been shunned by Western countries because it carries out suicide attacks against civilians inside Israeli cities.
"We believe the Saudi position ... will be extremely important in breaking the embargo that America and Israel want to impose on our people"
Izzat al-Rashiq, a member of Hamas politburo
Although Saudi Arabia is a major Arab ally of the United States, withholding aid is seen as politically impossible for the government because of popular support for the Palestinians, not least now that an Islamist group has come to power.
The kingdom has traditionally sought to champion Muslim causes, at various points backing Mujahidin fighters in Afghanistan, Bosnian Muslims in the Balkan country's 1992-95 war, and Chechens against Russia.
Saudi media said the five-man Hamas delegation - which is headed by leader-in-exile Khalid Mishaal - would go on to visit Yemen, Bahrain and Kuwait, probably leaving Riyadh on Sunday after a meeting with King Abdullah.