"Stop the bloodshed, stop using weapons against your brothers, and unite," Haniya told a crowd of about 20,000 gathered in Gaza City after prayers for the Eid ul Fitr feast marking the end of the holy month of Ramazan.
Supporters of his ruling Hamas movement and Abbas's rival Fatah faction have clashed repeatedly since the routed Fatah from power in January elections, with the confrontations increasing during the past weeks.
On Sunday, a member of the security services loyal to Abbas was killed in clashes with Hamas forces, two days after gunmen opened fire near Haniya's convoy, the latest of more than two dozen people killed in the internecine violence.
The Hamas-Fatah rivalry has been exacerbated by the international political and financial boycott of the Hamas administration, which has dried up funds for the Palestinian government and plunged the territories into unprecedented crisis.
The West has demanded that the recognise Israel, renounce violence and agree to abide by past peace deals to unblock the badly-needed funds, but Hamas has steadfastly refused to do so.
"It is not the first siege imposed on the Palestinian people and on Palestine, but it is the first under which we will make no concessions, we will not fall," Haniya declared on Monday.
"It is the first siege during which we say 'no' to America, 'thousands times no' to concessions on Palestine," Haniya said.
"We will not bend. We are dying, but we will not cede a step from Jerusalem, our rights and the right of return for refugees," he said, to approving chants of "Allah Akbar!" (God is the greatest).
"Many homes are living in sadness. Some of them, who could not do their charitable duty, cried last night and could not feed their children," he said.
"Any other people, faced with such a siege, such difficulties, such destruction, would have given in."
Hamas's refusal to recognise the Jewish state, even implicitly, has led to fruitless months-long talks between Haniya and Abbas over forming a national unity government which could restart the funds to the beleaguered Palestinian territories.
Amid the stand-off and clashes, the two leaders seemed to head toward further escalation last week as they traded warnings over security forces in the occupied West Bank.
Abbas brought back an authoritative strongman of his late predecessor Yasser Arafat, Ismail Jaber, to head the security services in the territory, following a vow by Hamas to deploy its paramilitary force there.
On the record, officials denied that the two moves were linked, but a close Abbas aide admitted under condition of anonymity that the appointment of Jaber "is an important decision at the moment when there is a conflict between the government and the presidency".
On Friday, Hamas's hard-line foreign minister, Mahmud Zahar, defended the movement's 5,500-strong "executive force" in the Gaza Strip and vowed to expand it to the West Bank.
"We are going to double the numbers of the executive force and we will deploy in the West Bank to prevent you from torching the (office of the) council of ministers, seizing members of parliament or closing hospitals and schools," Zahar said, addressing Fatah loyalists.
Fatah vowed to prevent the deployment.
"We reject the presence of this force in the West Bank and we will prevent it as it is devoid of any legality," said Jamal Tirawi, Fatah spokesman in Ramallah and head of Al-Aqsa Martyrs Brigades, an armed group close to the faction.
"The Al-Aqsa Brigades have examined this decision and have come to the conclusion that any such force will be treated like a band of criminals," warned.

Copyright AFP (Agence France-Presse), 2006