Israeli forces say they came under fire as they escorted police officer who they said was searching for stolen cars in a refugee camp south of the West Bank city of Ram Allah.
Three soldiers and a police officer were wounded, one seriously, the statement said.
The Israeli troops say they launched house-to-house searches.
The incident occurred in al-Amari refugee camp in Ram Allah.
The shooting came three days after Palestinian groups said they would extend an informal truce agreement until the end of the year after three days of negotiations in Cairo with the Palestinian leadership.
There was no immediate claim of responsibility for the shooting.
In the other incident, soldiers shot and wounded a Palestinian civilian at an Israeli army roadblock near the West Bank town of Bethlehem.
An Israeli police spokesman alleged the man tried to steal a gun from an Israeli police officer at the heavily guarded checkpoint.