"We know that in addition to the soldier and bomber, two Palestinian civilians were also killed," the spokesman said.
The Palestinian victims were the driver of the taxi that the bomber had been travelling in and another passenger.
West Bank medical sources said that five Palestinians were also wounded in the blast.
Aljazeera's correspondent in Tulkarm, Mueen Shadid, said six Palestinians, including a woman, were injured in the attack.
Witnesses said the wounded might have been shot by Israeli forces, often accused of indiscriminately shooting at people.
The impact of the blast was so huge that the Israeli army had initially said it was the work of two bombers.
The Israeli military said the bomber had been travelling in a taxi which was stopped at an impromptu checkpoint.
"Three passengers exited the taxi, including the bomber who was wearing a large overcoat," an Israeli army spokesman said.
"The roadblock commander requested that the bomber open his coat to be searched. The bomber then opened his coat and detonated an explosives belt concealed under his coat."
The belt had been wired to a large amount of explosives and was packed with nails and other shards of metals.
The Israeli army said that the bomber had intended to blow himself up in a crowded public place after crossing the border into Israel.
"This suicide bombing, which had been intended to be carried out in a heavily populated civilian location inside Israel during a national holiday, was prevented due to the effectiveness of the security measures taken in light of the intelligence information," it said in a statement.
There was no immediate claim of
responsibility for The attack
Israeli forces had been placed on a state of alert over the possibility of an attack inside Israel during the Hannukah festival of light which ends on 2 January.
The bomber came from a village in the Tulkarem area, a stronghold of Islamic Jihad. There was no immediate claim of responsibility for Thursday's attack, however,
After the attack, about half a dozen Israeli military vehicles converged on the scene. The army imposed closures on the Palestinian West Bank towns of Tulkarem and Qalqiliya, preventing people from coming in and out.
Nabil Abu Rudeina, a Palestinian Authority spokesman, condemned the attack as counter-productive.
"The operation in Tulkarem was against the national interests of the Palestinian people," he said.
"We should not give Israel any pretext to continue the escalations against the Palestinians."
Zeev Boim, Israel's deputy defence minister, pointed the finger at Syria over the attack.
"We should not give Israel any pretext to continue the escalations against the Palestinians"
Nabil Abu Rudeina,
Palestinian Authority spokesman
He said Damascus "encourages terrorism" in order to "deflect international attention" away from the ongoing probe into the assassination of Rafiq al-Hariri, the former Lebanese prime minister.
The latest deaths brought the overall toll since the start of the Palestinian uprising in September 2000 to 4922, more than three-quarters of them Palestinians.
The bombing came hours after Israeli warplanes and artillery pounded the northern Gaza Strip, beginning an aggressive new campaign to stop Palestinian rocket fire.