By Nidal al-Mughrabi

GAZA (Reuters) - Israeli forces killed nine Hamas militants in the Gaza Strip on Tuesday and the Islamist group's armed wing issued a statement claiming responsibility for its first suicide bombing in Israel since 2004.

An Israeli air strike on a Hamas security compound killed seven of the militants, whom the group said were holding afternoon prayers. Two other armed members of the movement, which controls the Gaza Strip, were shot dead by Israeli soldiers near the border with Egypt.

The Israeli army said it was responding to Palestinian rocket attacks on southern Israel.

Hamas's Izz el-Deen al-Qassam Brigades issued a formal statement claiming "full responsibility" for Monday's suicide bombing in the southern Israeli desert town of Dimona, where a top-secret nuclear reactor is located.

An Israeli woman was killed, along with the Palestinian suicide bomber. Another attacker who was shot dead by police.

Hamas, which seized Gaza in June after routing Palestinian President Mahmoud Abbas's secular Fatah forces, identified the attackers as Mohammed al-Herbawi and Shadi Zghayer, both from the West Bank city of Hebron.

"I never expected Mohammed to carry out a martyrdom attack. He was quiet and normal. I was shocked when I saw his name on ... television," his weeping mother, Um Samer, told Reuters.

Both men served about two years in Israeli jails and were known in Hebron as Hamas supporters.

Abu Ubaida, spokesman of the Izz el-Deen al-Qassam Brigades, said the bombing was in response to "massacres by the occupation." He singled out the killing of 18 Gazans, including the son of Hamas leader Mahmoud al-Zahar, by Israeli forces last month.

Hamas opposes Abbas's peace talks with Israel, but top Israeli and Palestinian negotiators, who met on Monday after the Dimona bombing, have vowed not to be deterred by the violence.

Israeli President Shimon Peres said Hamas's actions could make it "impossible" to create a single Palestinian state in Gaza and the occupied West Bank, where Abbas's Western-backed government is based.

A senior member of Prime Minister Ehud Olmert's party, Tzachi Hanegbi, urged the Israeli government to step up its fight against Hamas by assassinating its political leaders.

"We do not fear threats of assassination, but we take them seriously and we prepare for the worst," spokesman Ubaida said.

A Hamas security officer said its members were ordered to take "all necessary precautions," including turning off cellular phones that could be tracked by Israeli drones that routinely fly over the Gaza Strip.

HAMAS LEADERS

The Israeli military has largely refrained from targeting Hamas's political wing in recent years, but has struck repeatedly against the group's field commanders.

Hanegbi said Israel's killing of Hamas leaders Ahmed Yassin and Abdel Aziz al-Rantissi in the Gaza Strip in 2004 had a "direct effect on the motivation of the Hamas leadership to continue to carry out suicide attacks," adding the tactic should be revisited.

"(Hamas's political leaders) have evidently forgotten the bitter fate (of Yassin and Rantissi) and therefore we should add the current leaders of the organization to that list," he said.

"There is no difference between those who wear a suicide suit and a diplomat's suit," he said.

Responding to Hanegbi's remarks, Taher al-Nono, a spokesman for Gaza-based Hamas political leader Ismail Haniyeh, said: "The threats are part of continuing Israeli terrorism and crimes aimed at achieving political gains."

(Additional reporting by Haitham Tamimi in Hebron, Ari Rabinovitch and Avida Landau in Jerusalem; Writing by Adam Entous and Jeffrey Heller in Jerusalem; Editing by Elizabeth Piper)