Palestinian doctors in Gaza say several people have been hurt in fresh Israeli air strikes there, that took place as Israel's Lebanon offensive continues.
Israel says it attacked buildings used by militants
Israel says it attacked buildings used by militants from Hamas and the Popular Resistance Committees in Gaza City and the northern town of Beit Hanoun.
Palestinian militants fired a rocket on Sderot in Israel, hurting one person.
Meanwhile, the Palestinian president is heading to Kuwait as part of efforts to negotiate an end to the violence.
More than 100 Palestinians have been killed, many of them civilians, in Israeli air strikes and incursions since Palestinian militants captured a young Israeli soldier more than a month ago.
Yet the intense attacks on Lebanon have overshadowed the continuing violence in the Gaza Strip, our correspondents say.
Palestinian President Mahmoud Abbas has been having talks with Egyptian President Hosni Mubarak, who has been playing a key role in mediating between Israel and the Palestinians.
Mr Abbas's visit to Egypt was the start of a regional tour that will take him to Saudi Arabia and other Gulf states.
The BBC's Lucy Williamson, in Gaza, says Mr Abbas has been sounding very upbeat about the possibility of a negotiated ceasefire in Gaza.
The sticking point all along has been how and when Palestinian militants will hand over captured Israeli soldier, Gilad Shalit, our correspondent says.
The Palestinian leader, left, and Egyptian president discussed Gaza
Militant groups, including Hamas, have said any handover will need to be accompanied by the simultaneous release of Palestinian prisoners currently being held in Israeli jails.
Israel has stuck to its demand that the soldier be released first.
According to a key negotiator, who has been acting as a mediator between Mr Abbas and the militant leaders, the idea being floated now is that a third party - probably Egypt - will take charge of the soldier, while Israel keeps its side of the bargain.
Even if this is accepted by militant groups, though, there is also a worry that the timing might prove tricky, our correspondent says.
The violence is increasing on Israel's northern border. And many Palestinians are very supportive of Hezbollah's actions.
Our correspondent says that while Hamas has stuck to its formal position that there is no linkage between the two conflicts, privately many in Gaza's political elite believe it could be difficult for them to agree to a deal with Israel while Hezbollah continues its fight in the north.
On Sunday, Mr Abbas reportedly condemned the deadly Israeli raid on the Lebanese village of Qana as a "crime" and asked the UN to oversee an immediate ceasefire.
Top Palestinian negotiator Saeb Erekat was quoted by AFP as saying: "Abu Mazen has called the Lebanese president and prime minister and offered his deepest condolences [for] the victims of the crime that was committed by Israel in Qana which he condemned in the strongest possible terms and that he had asked the permanent members of the [UN] security council to provide for an immediate ceasefire in Lebanon."