"We will do all we can to prevent these rockets," Abbas told reporters in Gaza as Israel threatened a ground offensive to halt attacks by the fighters. The violence threatens a five-month-old truce and a planned Israeli Gaza pullout next month.
Abbas's police forces have also engaged in their deadliest clashes with the group in years in an effort to stop the rocketing since an attack killed an Israeli woman in southern Israel on Thursday.
The Israeli military has killed at least eight Hamas members since Friday, in the first assassinations in seven months.
Israel has signalled that despite a large troop buildup near Gaza at the weekend, it would not immediately launch any ground raid.
Abbas cautioned that any Israeli raid into Gaza at this time "could undermine everything and sabotage everything," referring to a shaky calm he had engineered with fighters after agreeing with Israel to a ceasefire in February.
Abbas said he has sought American mediation to prevent an Israeli incursion into Gaza.
Hamas has launched rockets
at Israeli towns
Hamas responded by saying it remained bound by a seven-month-old informal truce despite launching a mortar attack on a Jewish settlement in the Gaza Strip that it said was revenge for Israeli assassination of one of its members.
"We confirm that we continue to be bound by the arrangements agreed in Cairo on a conditional cooling down, but we reserve the right to retaliate in the event of enemy (Israeli) attacks," Hamas leader Said Syam said after talks with an Egyptian delegation.
"If the enemy halts its attacks, we won't have to retaliate any more, even though we are continuing to resist."
Egypt's deputy intelligence chief, Mustafa al-Buheiri, had rushed to Gaza in an effort to rescue the teetering truce.
Syam said it was "premature" to talk of a meeting with Abbas, who met the Egyptian delegation earlier.
"In the meantime, we'd like the Palestinian Authority to put pressure on the Zionist enemy to halt its aggressions," Syam said.