Abbas ordered security forces to deploy across Gaza after three sons of one of his supporters were killed on Monday on their way to school.
Tension between Abbas's Fatah movement and the governing Hamas party soared after the attack by unidentified assailants.
Early on Tuesday, heavily armed members of the security forces that take their orders from Abbas took up positions around key installations and road junctions in Gaza City.
"Palestinian security forces deployed in all streets of Gaza City to prevent crime. This was upon orders from President Abbas," a Palestinian security source said.
Security forces loyal to the Hamas government also strengthened their positions. There was no immediate sign of friction between the Abbas and Hamas loyalists.
Scores of children on their way to school paid their respects at a mourning tent erected in Gaza City for the dead boys. They then set fire to tyres in the streets to protest against the killings.
Mourners firing guns stormed the parliament compound on Monday during the funeral for the boys, aged six to nine.
"Instead of dismissing the Hamas-led government, he[President Mahmoud Abbas] should resign and call for early presidential elections."
Drmuniruddin, Dhaka, Bangladesh
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A senior Palestinian intelligence official in the occupied West Bank said it was unclear who was behind the attack on Colonel Baha Balousha's children.
Besides internal political unrest, Gaza has been divided by clan fighting and a surge in crime since the imposition of a Western aid embargo on the Hamas government increased poverty.
Abbas and Ismail Haniya, the Palestinian prime minister, said they had urged the authorities to find the killers.
Political tension has been rising over the failure of Hamas and the formerly dominant Fatah movement to form a unity government that Palestinians hope might end the Western boycott.
Abbas aides said on Saturday that the president planned to call early elections after talks on a unity government foundered. Hamas accused Abbas of trying to topple the government, which came to power after beating Fatah in elections last January.
Unity talks broke down over Hamas's rejection of Western demands that it recognise Israel, and its insistence on holding the interior and finance portfolios in any new government.
Abbas was elected separately in early 2005.