The Palestinian Authority President, Mahmoud Abbas, has held his first round of talks with the militant group, Hamas.
Mr Abbas, who is on a three-day visit to Gaza, is trying to persuade the group to stop attacking Israel so that the peace process can move forward.
Afterwards a Hamas spokesman described the meeting as very positive, saying that the group had listened with an open mind to Mr Abbas's appeal for calm. More talks are planned.
Yesterday, a Hamas suicide bomber killed an agent of Israel's Shin Bet security service and wounded seven other Israelis in a blast at an army checkpoint near the Gush Katif Jewish settlement in Gaza.
Israel is demanding that Mr Abbas act immediately to halt the violence.
A senior Palestinian commander has said the Authority's security forces will deploy to Gaza's borders with Israel within days to enforce Mr Abbas's order that militant attacks must stop.
