Exchange of fire
After the explosion, tanks stormed into Gaza near the town of Deir Al-Balah, with an exchange of gunfire erupting between the soldiers and Palestinian fighters, witnesses said.
Later on Thursday, four members of Islamic Jihad died when Israeli aircraft launched an attack near the town of Khan Yunis.
"We opened fire this evening on the terrorists who were trying to place explosive charges near the area where the attack [took place]," an Israeli army spokesman said.
Another Palestinian had been killed in an Israeli air raid in the northern town of Jabaliya earlier in the day, Palestinian medical workers said.
Israeli forces had withdrawn from northern Gaza on Monday after a series of deadly raids targeting Palestinian rocket crews left more than 125 people dead - half of them civilians, according to medical officials.
On Thursday, a number of rockets fired from the Gaza Strip landed in the Israeli town of Sderot injuring at least one person and setting a house on fire.
Hamas-Egypt talks
The Israeli soldier's death at the Kissufim crossing came on a day delegations from Hamas and Islamic Jihad crossed the border at Rafah into Egypt for talks on the situation.
Sami Abu Zuhri, a Hamas official, said the onus was on Israel to first make a commitment to stop "all forms of aggression" and end its blockade of the impoverished coastal enclave.
"The ball is in Israel's court," he said.
Khader Habib, an Islamic Jihad leader, said the group sent a team to Egypt for "talks about calm".
"The conditions are clear, the Zionist enemy must end all forms of aggression against our people in Gaza and the West Bank and lift the siege on Gaza," he told the Reuters news agency.
At the same time, David Welch, the US Middle East envoy, was in Cairo meeting Ahmed Abul Gheit, the foreign minister, to discuss how a ceasefire could be achieved, the Egyptian foreign ministry said.
The last time Israel and Hamas agreed to a mediated truce was in November 2006, after a five-month Israeli offensive in Gaza that followed the seizure of an Israeli soldier by militants.
Thursday's developments follow the latest visit by Condoleezza Rice, the US secretary of state, to the region, during which she said that she had secured a pledge from Israel and the Palestinians to resume peace talks.
Relations with Israel were suspended by Mahmoud Abbas, the Palestinian president, to protest against the Israeli raids.
Abbas has called for a ceasefire between Israel and Hamas, but at a news conference with her Israeli counterpart Tzipi Livni on Wednesday, Rice said that a truce was not a condition for the resumption of talks.