A spokesman for Islamic Jihad said his group carried out the attack in cooperation with the Al-Aqsa Martyrs' Brigades, an offshoot of Palestinian President Mahmoud Abbas's more secular Fatah faction. Jihad described the attack as a successful martyrdom operation.
An Israel Defense Forces spokeswoman confirmed that there had been an explosion in the area. No IDF soldiers were hurt.
The explosives-laden truck may exploded on the Palestinian side due to a technical failure. As it approached the border, other militants fired mortar shells at the crossing.
Shortly after the explosion, the Israel Air Force attacked a vehicle carrying several Palestinians that were apparently connected to the attempted attack. The IDF said two militants were killed in the strike.
Abu Ahmed, a spokesman for Islamic Jihad's armed wing, said the truck was carrying four tons of explosives. He identified the suicide bomber as 23-year-old Ibrahim Nasser from Jabalya in the northern Gaza Strip.
Hamas, which controls the Gaza Strip, said the vehicle was driven by a suicide bomber under cover of heavy early morning fog and that he was accompanied by gunmen.
Residents in the Gaza Strip who live over 30 km (20 miles) from the crossing reported hearing the blast.
Israel's Channel 10 television said troops had prevented the truck from getting close to the crossing by firing at it before it exploded.
Thursday's incident was one in a string of recent Palestinian militant attacks on Israeli crossings on the Gaza border. Last month, on the eve of Passover, Hamas gunmen wounded 13 Israeli soldiers in a well-coordinated assault by explosives-laden vehicles against the Kerem Shalom crossing.
One week prior, Gaza militants killed two Israeli civilian workers at the Nahal Oz crossing's fuel depot.
Israel has heavily restricted the movement of Palestinian people and goods through its border crossings with Gaza since Hamas seized the territory from Fatah in fighting last June.
In Egyptian-mediated talks on a truce between Israel and Palestinian militant groups, Hamas has demanded the crossings be re-opened in return for a cessation of violence.
"Resistance is strong and we are not begging for calm," Abu Ahmed said after the attack.
Separately, but at the time of the bombing, IDF troops raided a village in the central Gaza Strip and shot dead a 63-year-old man, medical workers and Hamas said.
An IDF spokesman had no immediate information on the incident. Israel frequently carries out raids and air strikes in the Gaza Strip as part of what it describes as efforts to curb Qassam rocket fire at Negev towns.