Girls’ school and medical centre in Nablus closed as part of crackdown on Hamas.
In agreeing to reopen the passages, Israel suggested it might stop automatically closing the crossings in response to every truce violation.
About a dozen rocket attacks have been fired into Israel over the last three weeks, but none have caused serious injuries.
Crossings were closed for about half that time.
In another development, Israel lifted a curfew on the Palestinian village of Nilin, a military spokeswoman said.
Ayman Nafi, the town’s mayor, confirmed that the soldiers had pulled out.
“We woke up and luckily we did not see their presence,” he said early on Tuesday.
“Now we are inspecting the damage they have inflicted on us.”
The curfew, which prevented residents from leaving their homes or traveling in and out of the village, was imposed on Friday after violent protests erupted over Israel’s West Bank separation barrier.
Israel said the barrier helps keep out Palestinian suicide bombers, who have killed nearly 300 Israelis since the intifada, or uprising, began in 2000.
But the network of fences and concrete barricades also loops around Jewish settlement blocs, cutting off some West Bank villages from their farmland.
Four years ago this week, the International Court in The Hague ruled that construction of the 720-km barrier on occupied land was illegal. The UN said Israel has ignored that non-binding ruling.