Earlier on Friday, Israeli occupation forces at the two crossings said they had closed the border citing security concerns.
An Israeli military source said: "They have closed due to a high security alert."
Palestinian Authority Director-General of Borders Salim Abu Safieh said Israel's military had not coordinated the closure with the Palestinian Authority (PA).
Abu Safieh highlighted the plight of thousands of Palestinians who are prevented from getting to work due to such closures.
Israeli occupation forces frequently shut borders and checkpoints.
Abu Safieh said the perception is that the Israeli army continues to use borders as a point of pressure against the PA. He said Israel should ease the restrictions on freedom of movement for Palestinians, the Palestine News Network (PNN) reported.
"Israel should commit to remove all those obstacles being imposed on the borders to prove its real intention to reach an agreement with the Palestinians," he said.
He accused the Israelis of failing to commit to their obligations and promises to provide facilities at military checkpoints and borders, the PNN reported.
Abu Safieh mentioned that Israeli declarations concerning an increase in the number of workers permitted to cross Bait Hanun checkpoint in the northern Gaza Strip, for example, are not applied.
Israeli forces often prevent
patients from entering Egypt
Only 2400 workers passed through the border, instead of the 5000 the Israelis claimed would be allowed passage.
At some borders, such as Al Muntar, the number of operating hours was increased, but the efficiency was not.
The number of delivery trucks and goods able to pass remains unchanged.
At the Bait Hanun border, which Israel calls the Erez crossing, between the industrial zones in the northern Gaza Strip, only 300 workers were able to cross, while the Israelis had said that 2500 workers would be granted permission.
Abu Safieh warned Israel that its violations, such as the firing of live ammunition at Palestinian homes from the Rafah border crossing, and the military obstruction of patients at checkpoints preventing them from reaching hospitals in Egypt or abroad, will negatively influence the truce.
Gaza, in the meantime, remains fenced-off with barbed wire by Israel.
Meanwhile, Aljazeera reported that Israeli occupation forces arrested seven people, including Palestinians, foreigners and Israeli activists, during a peaceful demonstration in Bilaid village west of Ram Allah.
The demonstration was against the building of the separation wall which will separate Palestinian villages from the West Bank.
The Israeli forces obstructed the demonstration from setting off after Friday prayers. They showered demonstrators with sound and teargas bombs, Aljazeera reported.
They also fired plastic bullets at the demonstrators, wounding many.
The demonstrators chanted slogans condemning the building of the wall and carried fake tombstones symbolising the death that the wall represents.