According to Israeli police the explosions were apparent human bombings as two of the bodies were of the bombers themselves.
"We have ten dead as well as the two bombers," police spokesman Gil Kleiman told reporters.
Police initially believed that the explosions were set off accidentally in a workshop in the port. The blasts were heard around 17:00 (15:00 GMT).
Rescue services spokesman Yerucham Mendola said "some of the victims were thrown a long distance" by the blasts. At least 20 people were injured in the blasts, eight seriously.
One of the bombers reportedly exploded just outside the main gate to the port. The second managed to enter the facility and detonated his bomb just a short time later in a centrally-located workshop inside the port.
It was the first attack of its kind at an Israeli seaport during more than three years of Israeli-Palestinian violence.
Palestinian resistance groups Hamas and al-Aqsa Martyrs Brigade - the military wing of Fath- have both claimed responsibility for the attacks, reported Aljazeera's correspondent.
In an interview with Aljazeera, a senior Hamas official said the attack came in retaliation "for the massacres committed by the [Israeli] occupation troops during March leaving behind 44 martyrs."
The Quraya/Sharon summit was
cancelled by Israel after the attack
The Hamas leader insisted that resistance will go in spite of "the security wall, the Zionist terrorism, and the US plots".
Hatim Abd al-Qdair, senior Fatah leader put the blame on Israeli Prime Minister Ariel Sharon. "Sharon is the one responsible as he insisted on his aggression and on building the separation wall," he told Aljazeera.
Abd al-Qadir denied the attack was intended to topple the peace process. "The Israeli initiative to withdraw from Gaza is vague and it was only created to delude the world as in reality there is only killing and violence."
A member of al-Aqsa Martyrs Brigades identified the assailants as Nabil Massud, 18, and Muhammad Salim, also 18, from the Jabaliya refugee camp.
Israeli Cabinet Minister Yosef Paritzky said that the assailants "found a weak point and exploited it".
"A port, by nature, is a very busy place. There are many people coming and going. It is impossible to seal the entire country hermetically."
Israeli Cabinet Minister
"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."
Ashdod is 40km north of the Gaza Strip, a hotbed of Palestinian resistance fighters who have vowed revenge after Israeli soldiers killed 14 people in a raid on 7 March.
A Palestinian bomber killed eight people aboard a Jerusalem bus on 22 February.
Due to the bombing the planned summit between the Israeli and Palestinian premiers has been cancelled, Israeli officials have said.
Aides to Sharon and his Palestinian counterpart, Ahmad Quraya, had met on Sunday and planned to meet again on Monday to finalise plans for the leaders' first summit since Quraya took office in October.
The summit had been tentatively scheduled for Tuesday.
After the bombing, Israeli officials called off the preparatory meeting and the summit, an official in Sharon's office said.
For its part, the Palestinian Authority condemned the attack and urged Palestinians to stop such attacks immediately.
Police initially believed the
explosions were set off accidentally
The Palestinian government also urged Israel to commit itself to a ceasefire "to break the cycle of violence" and to
implement the US-backed "road map" for peace in the Middle East.
"We condemn the targeting of civilians on both sides and the
continuation of the military escalation," Quraya and his government said in a statement.
"We call again on the Israeli government to stop the exchange of fire between the two sides as soon as possible" the statement added.
Such attacks worked against the Palestinian national interest as they served to give the Israelis an excuse "to continue their aggressions and build the wall," it added in reference to Israel's West Bank separation barrier.