Police said the bombers may have intended to blow themselves up near chemical tanks to try to cause far greater loss of life. The bombings raised serious questions about Israel's vulnerability; Israel has been fearing a so-called "mega attack" on a chemical depot or fuel storage facility.
Police ordered increased security at all Israeli seaports, airports and train stations after the attack, and Israel Radio reported that the overall terror alert was at its highest level.
Israeli Prime Minister Ariel Sharon consulted with his army chief of staff over an Israeli response to the bombing, Army Radio reported.
Area police commander Moshe Karadi told reporters that the explosives used were "different from other such cases." Israel TV said they were high-grade plastic explosives not used before in Palestinian attacks, indicating a deadly upgrade for future operations.
The attackers, residents of a Gaza refugee camp, were the first Palestinian bombers from Gaza to infiltrate into Israel during the current round of violence. The volatile coastal strip is surrounded by a fence and subject to stringent security.
Sharon called off a meeting with his Palestinian counterpart, Ahmed Qureia, that had tentatively been set for Tuesday. Preparatory talks set for Monday were also called off, a Sharon aide said.
Palestinian Cabinet minister Saeb Erekat condemned the attack on behalf of the Palestinian Authority and expressed regret that Israel canceled the talks.
Sunday's bombings could signal a change in tactics, with Palestinian militants trying to carry out even deadlier attacks. Many of the bombings since 2000 targeted buses, cafes and markets, where a large number of people gather. The deadliest of those attacks killed 30 people.
Sharon aide Raanan Gissin said the target was no surprise because terrorists had long been trying to carry out a massive bombing, "and today was another effort to carry out such an attack."
A major power station was also nearby. Government officials said they would investigate how the attackers were able to get into such a sensitive facility.
"They found a weak point and they exploited it," Israeli Cabinet Minister Yosef Paritzky said of Sunday's assailants. "A port, by nature, is a very busy place," he said. "There are many people coming and going. It is impossible to seal the entire country hermetically."
The bombings Sunday happened before 5 p.m. (1500 GMT), one outside the perimeter fence and one inside a workshop inside the fence.
"One of our workers who was lightly wounded told me that the terrorist came in and asked for water and the moment he showed him where there was a tap he blew up," said Sami Pinto, a port worker.
Morris Rima, who works at a nearby haulage company, ran toward the scene. "When I arrived here I saw body parts strewn around, some of them hanging on the barbed wire," he said.
Eleven people were killed, in addition to the bombers, and 18 were wounded.
Karadi said the bombers have been trying to blow themselves up next to tanks of bromide or other dangerous chemicals stored in the port. The explosions went off some way from the chemical storage area, possibly prematurely, he said.
In 2000, Palestinians tried to blow up Israel's main fuel depot, outside Tel Aviv, setting off explosives under a tanker truck. The fuel did not ignite, but officials warned that a successful attack of that type might have resulted in thousands of casualties.
All Palestinian bombers since 2000 came from the West Bank, which has a much more porous border with Israel. Israel is building a barrier in the West Bank aimed at stopping attackers, but Palestinians object to the planned route, which cuts deep into territory they claim for a future state.
Hamas and the Al Aqsa Martyrs' Brigades, militants with links to Yasser Arafat's Fatah party, claimed joint responsibility for the attack.
The Ashdod bombers were identified as Nabil Massoud, 17, and Mahmoud Salem, 17. They were classmates in the 11th grade of a high school in the Jebaliya refugee camp, a large shantytown near Gaza City and a hotbed of militancy. The teens' fathers said they were proud of their sons.
The militant groups said the attack came in response to Israeli killings of Palestinian militants.
After evening prayers, worshippers streamed out of mosques on along the road from Jebaliya to Gaza City celebrating on the streets and shouting Hamas slogans.
In recent weeks, militants appeared to be stepping up efforts to infiltrate Israel. On March 6, Gaza militants attacked the Erez crossing into Israel with a taxi and two vehicles disguised as Israeli military cars. The four militants and two Palestinian police were killed.
Abu Qusay, an Al Aqsa leader in Gaza, said Sunday's attack was meant to show that "we can reach any place in Israel, even the heavily protected places, such as a port or airport."
Sharon said last month that in the absence of peace moves, Israel will implement his "disengagement plan," which includes the evacuation of Gaza Strip settlements.
In preparation for the possible withdrawal, the Palestinian Authority has drawn up a security plan for Gaza that would ban militants from carrying arms in public, according to a copy obtained Sunday by The Associated Press.
The plan, finalized March 4 after discussions with Egyptian officials, would also leave Palestinian leader Yasser Arafat's cousin, Moussa, as head of a new security force of 700 soldiers that would maintain order on the border of Egypt and Gaza, Palestinians security sources said.
The proposal was presented to Palestinian militant groups last week for comment. There has been some concern that an Israeli pullback could leave a power vacuum in the volatile coastal strip and lead to chaos. Egypt also fears disorder along its border with Gaza.
Under the proposal, which details steps over a five-week period, Palestinian security forces will begin enforcing traffic laws, protecting government ministries and demanding people pay for water and electricity. By the fifth week, the Palestinian Authority will declare it is illegal to carry guns in public.
Since Sharon's announcement, violence between Israelis and Palestinians — and among competing Palestinian factions — has increased in battles for power in advance of the proposed withdrawal.
On Sunday, Israeli forces killed three Palestinian militants near the Israeli settlement of Netzarim in Gaza, the army said. Soldiers searching the area after the shooting discovered explosives on the men's bodies, according to the army.