The Islamic militant group Hamas claimed responsibility for a West Bank blast, its first open violation of a unilateral cease-fire it declared June 29, while renegades in Yasser Arafat's Fatah movement said they had carried out the other attack.
Israeli Prime Minister Ariel Sharon said he would not move forward with an already troubled U.S.-backed peace plan "if terrorism doesn't cease completely."
However, the militants and Israeli military officials hinted they would try not to escalate the situation, possibly to avoid being blamed for any collapse of U.S. peace efforts.
Hamas said it had carried out the bombing to avenge the killing of two of its members by Israeli troops last week, but would now return to observing the truce. An Israeli military source said there would be no large-scale retaliation.
The bombing at the entrance to the West Bank settlement of Ariel killed the assailant and an 18-year-old Israeli army recruit. The explosion seriously injured two others, whom rescue services identified as teenagers.
"I saw the terrorist on the ground and another young man or girl killed and two others wounded," said the mayor of Ariel, who arrived shortly after the bombing.
Less than an hour earlier, another bomber blew himself up outside a supermarket in Rosh Haayin, a town in central Israel. The attacker and an Israeli were killed. Nine people were injured, one seriously, five moderately and three lightly.
"I saw fire and a cloud of smoke. They brought out an injured child and then his mother," said Avigail Josef, who sells lottery tickets in a booth just feet from the supermarket.
The blast left a mass of twisted blinds and shattered glass and sparked a large fire in the supermarket. Firefighters with breathing equipment pulled casualties out of the shattered store.
"We heard an explosion and I ran downstairs and saw smoke," a witness identified as Roni told Israel's Channel 2 television. "I saw the bomber only the upper part of him was intact, he was missing legs and arms. I saw a leg lying nearby," he said.
The attacks marked the most serious truce violations yet. An army commander said they had apparently not been coordinated.
Hamas initially said Islam Yousef Qteishat, the Ariel assailant, was 21, but the family later said he was 17. The second attacker was identified as Khamis Ghazi Gerwan, 17, a Fatah follower.
One was from the West Bank city of Nablus and the other from the nearby Askar refugee camp. The two lived just a few blocks apart, but their families said they did not know each other.
Israel sealed Nablus, and imposed a curfew on surrounding villages.
Israel also called off the planned release of 76 Palestinian prisoners, none of them involved in anti-Israeli violence, who were to have been freed Tuesday. Some of the detainees had already boarded buses when they were called back.
Israel accused Palestinian Prime Minister Mahmoud Abbas of not doing enough to prevent attacks.
"We can't be expected on the one hand to continue to make concessions and on the other hand to receive more suicide bombings," said Israeli Foreign Ministry spokesman Jonathan Peled.
"We will continue to take every measure necessary to protect our civilians as long as the Palestinian Authority doesn't begin seriously fighting against the terrorist infrastructure," he added.
Under a U.S.-backed peace plan, the Palestinians must dismantle militant groups, but Abbas, also known as Abu Mazen, has said he will not confront Hamas, Islamic Jihad and Fatah's Al Aqsa Martyrs' Brigade. Abbas is currently touring Gulf states.
"The fact that Abu Mazen is circling the globe does not show a serious commitment to dealing with terrorism," said Israeli Cabinet minister Gideon Ezra.
The Palestinian leadership condemned the bombings, but said the Israeli accusations were unfair. The Palestinian security chief, Mohammed Dahlan, said he will not permit truce violations and that suicide bombings harm the Palestinian interest.
Rosh Haayin is very close to the "green line" between Israel and the West Bank, reports CBS News Correspondent Allen Pizzey, making it relatively easy for suicide bombers to cross.
Regional police chief Uri Bar Lev said police had been on high alert after warnings of an attack in the area. Israel TV's Channel 10, citing a Palestinian security source, said Palestinian officials had warned Israel about the Rosh Haayin and Ariel attacks.
An Israeli security official said that since the June 29 cease-fire, the military had thwarted 36 Palestinian attacks and arrested more than 200 Palestinians.
Tuesday's were the first suicide bombings since a Palestinian from a splinter cell within the Islamic Jihad group blew himself up inside a house on July 7, killing a 65-year-old woman.