An earlier helicopter strike damaged a Palestinian radio station in Gaza City affiliated with the Hamas faction, damaging the offices but causing only minor injuries.
"We know we can't achieve military equality," said Salah Bardawil, a Palestinian legislator who serves as spokesman for the Hamas faction in parliament.
He had been convicted of helping Israel kill several senior figures in the Hamas faction during the 1990's.
That day, Israeli military officials said they had killed an armed member of the Hamas faction, although they did not identify Mr. Abu-Laymoun by name.
Israeli military officials said that about 11:30 a.m., forces opened fire on three armed men from the Hamas faction in a field in the village of Taluza, north of Nablus.
At that point, a Hamas faction known as the Izzedine al Qassam Brigades issued a pamphlet in the territories.
In the 2005 Palestinian municipal elections, the Reform and Change list representing the Hamas faction won 73.4% of the vote, gaining the majority of the municipal seats (13).
Israel has repeatedly detained members of the Hamas faction in the now-defunct Palestinian parliament, chosen in 2006 elections in the West Bank.
Mr. Bardawil, a spokesman for the Hamas faction in the Legislature, said Israel's actions were increasing the popularity of Hamas.
The Palestinian president, Mahmoud Abbas, intends to call a referendum on a proposal developed by prisoners for a unified Palestinian political program that the governing Hamas faction opposes.