Azzam al-Ahmed, the head of Fatah's parliamentary bloc, said: "Hamas knows very well the details of what has happened. It knows Fatah was not involved in the explosions that took place."
Hundreds of people attended a funeral procession on Saturday for the Hamas fighters killed by the explosion.
Overnight, heavy fighting took place in Gaza's Tel al-Hawa district, where Hamas members confronted the family of a man they sought to arrest, exchanging fire and volleys of rocket-propelled grenades.
The office of Ziad Abu Amro, an independent Palestinian MP, was stormed by Hamas security forces who also confiscated his car, according to reports.
Hamas said in a statement on Saturday: "This criminal act proves that the call for dialogue from Ramallah [Abbas' headquarters] was a lie designed to throw sand in our eyes and conceal a conspiracy to kill and assassinate and terrorise our security forces."
Fatah responded by saying it had "no link whatsovever with internal disputes within Hamas," and accused elements within the armed wing of Hamas of planting explosives as part of an internal conflict.
Ahmed said: "Hamas' accusations aim at misleading the public opinion and at the same time ignoring Abu Mazen's [Abbas'] call for commitment to end the state of division and sit at the Palestinian negotiations table."
Al Jazeera's Ashraf Amriti, reporting from Gaza, said: "A lot of what happened a few moments ago shows how intenses things are in Gaza. Even now, Hamas has put up roadblocks to stop people, asking for their IDs".
Amriti said that the attacks are widely condemned by all the Palestinian factions who are working hard to reconcile the disputed parties.
The five men killed in the blast were members of the Izz al-Din al-Qassam Brigades, Hamas' armed wing.
Up to 20 other people were said to have been wounded in the blast, medical officials said, most of them on their way to the beach.
|The explosion was the third of its kind in Gaza in one day [AFP]
Iyad al-Hayya, the nephew of Khalil al-Hayya, a prominent Hamas leader, was among the dead.
Amar Mosbeh, a senior leader of Hamas's military wing, was also killed.
The Izz al-Din al-Qassam Brigades blamed "members of the fugitive party" - a term which usually refers to Fatah.
Another person was killed in Gaza earlier in the day as a bomb he allegedly tried to plant outside a cafe exploded.
Khalil al-Hayya said: "We have information that some elements are planning to carry out bombings against the interests and leaders of Hamas in order to sow anarchy."
Ahmed said this person had nothing to do with Fatah.
"Let them [Hamas] identify him in public, because we know him and we know his political affiliation. He is, in no way, related to Fatah movement."
Hamas called on Gaza residents to turn out in their masses for the funerals of those killed, who would be buried following noon prayers on Saturday.
The Izz al-Din al-Qassam Brigades also said that several suspects outside of Fatah had been arrested in the Gaza Strip without giving further details.
Among those seized was a cameraman for German television ARD, Sawah Abu Safeh, Palestinian officials said.
The explosions mark one of the biggest flare-ups in internal Gaza violence since Hamas forced out Fatah to seize control of the territory a year ago.
The factional violence has eclipsed Israeli-Palestinian fighting in Gaza, where an Egyptian-brokered truce has largely held since last month despite some violations on both sides.
The ceasefire stoked occasional intra-Palestinian tensions as Hamas has sought to prevent other groups from firing rockets across the border into Israel.