Egypt has been trying to broker a truce between Israel and Hamas, a Palestinian organisation which has de facto control of Gaza, to avoid an escalation in violence near the Gaza border.
The air raids came shortly after Israeli forces shot and killed a 16-year-old boy near the occupied West Bank city of Nablus.
Michal Ya'akov, an Israeli military spokesman, said he saw a man acting strangely at the Hawara checkpoint on Monday, which caused the soldiers to believe he was armed with explosives.
"A young Palestinian who seemed confused arrived at the checkpoint. When he reached the turnstile I stopped him and asked that he pass through the metal detector. The apparatus beeped when he went through," he said.
The suspect then ignored orders to stop and the troops opened fire on the youth, killing him, other Israeli sources said.
Ya'akov said the army later detonated five pipe bombs which were placed inside a belt in a controlled explosion at the scene of the shooting.
An Israeli military spokeswoman told reporters that it was clear that the man was intending to attack the checkpoint.
"There were no other Palestinians in the area when he tried to blow himself up, from his behaviour it appeared as if he was not intending to get into Israel but wanted to blow himself up at the checkpoint and attack the soldiers there," she said.
A Palestinian security source in Nablus said the person killed was from the village of Beit Furik near the city.
Israeli troops later entered the village to search for the house of the attacker's family, local residents said.