Deadly new attacks in the West Bank and Gaza Strip will not derail the peace mission of U.S. envoy Anthony Zinni, a White House spokesman said Wednesday.

Zinni had asked Israelis and Palestinians to observe two days of calm to help lower tensions and rebuild trust, a U.S. official said.

But a day after that request, Palestinians fired on an Israeli bus in the West Bank and suicide bombers set off their explosives in the Gaza Strip in double attacks near Jewish settlements that killed at least eight people and wounded about 30.

The State Department condemned the attacks and focused on Yasser Arafat, the Palestinian leader, as the one who should curb the violence.

"We stress it's absolutely imperative that Chairman Arafat and the Palestinian Authority act immediately, undertake all possible measures to pursue and apprehend those responsible for these horrific actions, and ensure that the organizations responsible are unable to commit further terror," spokesman Richard Boucher said.

"We're deeply troubled by the fact that these groups continue to have freedom to conduct their actions," Boucher said.

On a related front, President Bush's national security adviser said terrorist wings of Hezbollah, the guerrilla group that attacks Israel from Lebanon, "is very much responsible for the problems that we are having in places like the Middle East."

Condoleezza Rice, in an interview with the Arab MBS-TV, said "this simply has to be cleared up."

She said the administration had told Lebanon and Syria that "it cannot be the case that you are supportive of the fight against Al Qaeda and then go ahead and support terrorist activities of Hezbollah."

Israeli helicopter gunships attacked a Palestinian refugee camp Wednesday morning in response to mortar fire on nearby Jewish settlements. Four Palestinian militiamen were killed and 20 bystanders wounded in the airstrike.

Zinni remains "committed to helping the parties find a way to begin the security talks and the president remains hopeful that the talks can begin," White House spokesman Ari Fleischer said.

"The latest violence underscores the need for Chairman Arafat and the Palestinian Authority to take every step possible to reduce the violence and bring an end to the terrorism that is plaguing the region," Fleischer said.