Palestinian president Mahmoud Abbas is expected to leave hospital on Sunday afternoon after a week of treatment for pneumonia, a Palestinian official and medical source said.
Rami Hamdallah was not injured in the explosion, which occurred shortly after his convoy entered the territory run by Hamas, a security source in the convoy said.
The visit this summer by the second in line to the throne "is at the request of Her Majesty's government and has been welcomed by the Israeli, Jordanian and Palestinian authorities", the palace said in a statement.
A source for the Islamic Jihad group said Arafat Abu Marshould, head of the faction's armed wing in central Gaza, was killed along with a senior associate and two other gunmen.
The visit follows concessions by Hamas after discussions with Egypt, which has urged it to take steps towards reconciliation with Palestinian President Mahmud Abbas's Fatah, based in the occupied West Bank.
Hamas called on Palestinian President Mahmoud Abbas on Tuesday to respond to the disbanding of its shadow government in the Gaza Strip by ending his sanctions on the impoverished enclave.
UN Secretary General Antonio Guterres spoke of what he called obstacles to peace when meeting Prime Minister Benjamin Netanyahu, including Israeli settlement building and the need for Palestinian leaders to condemn "terrorism".