Speaking after the rocket attack on Sderot, Christopher Gunness, spokesman for the Office of the UN Special Coordinator for the Middle East Peace Process, said: "They (the rockets) landed a few hundred yards away from where we were."
Arbour arrived in Sderot after a visit to the Gaza Strip as part of a five-day tour of the Palestinian territories and Israel.
Israeli forces also entered the nearby Jabaliya refugee camp, as well as the northern town of Beit Lahiya.
Hospital officials named the dead fighter as Aiman Hassanein, a senior member of the governing Hamas organisation.
Witnesses said he was killed during an exchange of fire and that his brother was detained by troops.
The incursion came hours after an Israeli missile attack on a car in Gaza killed two Hamas fighters and injured five bystanders late on Monday night.
Hundreds of Palestinians gathered around two homes of Hamas and Islamic Jihad fighters after the Israeli military warned that the buildings would be destroyed in air raids, a security source said.
The source said: "They formed a human chain to prevent the two houses from being destroyed."
Hamas's armed wing hailed the success of human shields, calling it a "national duty" for Palestinians to protect the homes of fighters from Israeli air strikes.
The Israeli defence minister, Amir Peretz, said on Monday that Israel would continue its military operations in Gaza but had no intention of reoccupying the area.