Israeli troops at the crossing point opened fire immediately after the explosion, but it was not clear if the Palestinians had been killed by them or by the blast, according to some reports.
The dead Palestinians are reported to be policemen.
Other witnesses said another car carrying Palestinian resistance fighters had also approached the Israeli position, provoking an exchange of fire in which occupants of the vehicle had been killed or wounded.
All crossing points between Israel and the Palestinian territories have been closed since last Thursday for "security reasons" during the Jewish Purim festival being celebrated on Sunday and Monday.
Earlier on Saturday, a Palestinian policeman was killed by Israeli occupation forces in a raid on the northern West Bank town and refugee camp of Tulkarm.
Thair Abu Sirriyah, 19, was hit by bullets from Israeli forces who opened fire on residents, including students on their way to school.
Israeli soldiers fired on
Sirriyah was hit while standing in front of the Palestinian police station. He was reported as not being involved in any confrontation.
Residents said the dead man was an unarmed Palestinian policeman in uniform, heading home at the end of a night shift and that troops had opened fire after being stoned by youths on their way to school.
The latest death brings the overall toll since the start of the Intifada, or uprising, in September 2000 to 3800, including 2846 Palestinians and 886 Israelis.
On Friday, a Palestinian teenager was seriously wounded in the head by Israeli occupation army gunfire near the northern West Bank town of Jenin, Palestinian medics and security sources said.
Abd Allah al-Awna, 13, was hit when Israeli soldiers opened fire at a group of stone-throwers, prostesting an army incursion in the village of Jabaa, near Jenin.
Israeli army has upped force
over Jewish holiday of Purim
An Israeli military official told AFP "after having been attacked by about 30 Palestinian protesters who were throwing rocks at them, the soldiers fired rubber bullets and tear gas to disperse the aggressors."
Israeli occupation forces in and around Palestinian cities have imposed a "closure" of the West Bank and Gaza Strip before the Jewish holiday of Purim, which ends on Monday.
Aljazeera's correspondent reported that the Israeli army were still stationed at the three main entrances of PA chairperson, Yasir Arafat's headquarters in the city.
"The soldiers are stopping Palestinian civilian cars and preventing its occupants from entering or exiting the compound," the correspondent added.
He said several new Israeli checkpoints had been set up in many West Bank cities and towns.