At least 300,000 people have turned out in Gaza City for a rally to mark 20 years since Hamas was founded.
Waving green flags and banners, crowds of Palestinian men, women and children filled a large square for the event.
Analysts say the turnout is seen as a vital test of support for Hamas, which seized control of the Gaza Strip in June from its Fatah rivals.
In a defiant website statement, Hamas's leader in exile, Khaled Mashaal, vowed the group would not renounce violence.
Speaking from Damascus, Syria, he said Palestinians were capable of mounting a new uprising against Israeli occupation, like the intifadas of 1987 and 2000.
"Whoever thinks that Hamas has reached a dead end is wrong," he added, in his anniversary message to the militant Islamist organisation's website.
Militant group formed in 1987 at the start of first intifada
Aims to drive Israeli forces from the occupied territories
Wants to set up an Islamic state on all of historic Palestine
Dramatically won parliamentary elections in January 2006
Refuses to recognise Israel's right to exist
He also said Fatah leader and Palestinian President Mahmoud Abbas, who heads a moderate government in the West Bank, did not have a mandate to negotiate with Israel.
Hamas Prime Minister Ismail Haniya told the crowd the "choice of resistance and jihad" was "the shortest path to liberate Palestine".
"This will not be achieved by way of negotiations and concessions and certainly not through... sitting at round tables or exchanging smiles with the killers and executioners of the sons of the Palestinian people."
Hamas, Mr Haniya added, did believe in dialogue but "on the basis of no victor, no vanquished and... without conditions".
A huge banner hung from a building near the scene of Saturday's rally read: "We will not recognise Israel."
The BBC's Bethany Bell in Jerusalem says the event is a show of strength by Hamas in a Gaza Strip facing deepening political and economic isolation.
Tensions between Fatah and Hamas remain high.
Eye on Fatah
The Hamas rally attracted more people than the estimated 250,000 Fatah supporters who filled the same square for a rally last month.
That event ended with several people dead after Hamas security forces opened fire on a hostile crowd.
Fatah has reportedly banned any celebrations being held in the West Bank to mark Hamas's 20th anniversary.
On Friday Hamas gunmen in Gaza seized a key adviser to the Palestinian prime minister, accusing the official of collaborating with Israel.
On the same day in Gaza City, three people were killed in an explosion at a Fatah-organised funeral. Fatah accused Hamas of being behind the blast.
Israel closed Gaza to all but vital supplies after Hamas seized power in the summer, creating what the World Health Organization has described as an "intolerable" humanitarian situation.
Regarded by Israel, the EU and US as a terrorist organisation, Hamas was founded in Gaza in December 1987, after the outbreak of the first Palestinian uprising against Israeli occupation.