Palestinian leader Mahmoud Abbas says he will "do his utmost" to stop Palestinian rocket and mortar attacks on Jewish communities.
Violence has escalated in Gaza following a series of rocket attacks
His comments come on a day of violence between Israeli forces and Palestinian militants in the Gaza Strip.
Israel has threatened to launch a ground offensive to stop further Palestinian rocket and mortar attacks.
In response Hamas said it is committed to a conditional calm but retains a right to "resistance and self defence".
Israel and Palestinian militants have blamed each other for the breakdown of a months-long truce this week.
On Sunday, several Israelis were injured by Palestinian fire on two Jewish settlements, Neve Dekalim and Gush Katif.
Later in the day, the Israeli army said it shot dead a Palestinian man as he approached the Jewish settlement of Netzarim, just south of Gaza City.
There have also been well over 100 Hamas rocket attacks on Israeli targets in and around Gaza in recent days.
In response to the attacks, an Israeli aircraft fired a missile at a car in the northern Gaza Strip. Witnesses said the occupants escaped.
Earlier, Israeli forces killed a local commander of the Palestinian militant group, Hamas.
The man, Saeed Seyam, was shot near his home in the town of Khan Younis. Palestinian security forces say he was targeted by an Israeli sniper operating in a nearby settlement.
Mr Abbas told reporters in Gaza that the Palestinian Authority would do all it could "to prevent these rockets".
He blamed Israel for the renewed tensions, and cautioned that any Israeli raid into Gaza "could undermine everything and sabotage everything".
After meeting with Egyptian mediators, a Hamas official also called Saeed Seyam said the group was committed to the truce, but had the right to retaliate for Israeli violations.
Israeli forces have been gathering on the border with Gaza
The BBC's Alan Johnston in Gaza says that on the surface there is little new in what the Hamas spokesman said but analysts in the Middle East believe that the group may now be ready to return to a degree of calm.
Hamas has gone to the brink but it may not want to be responsible for provoking a major Israeli onslaught, our correspondent says.
Israel has been amassing tanks and troops in preparation for what could be large-scale incursions into Palestinian towns.
Prime Minister Ariel Sharon, who has promised a "strong and harsh" response to the attacks if they do not stop, said he had told military officials "that there are to be no restraints on our operations".
However, he said that the Palestinians attacks would not stop next month's planned withdrawal of Israeli troops from the Gaza Strip.
A Palestinian suicide bomber killed four Israelis in the town of Netanya on Tuesday, shattering months of relative calm in Israel.
Israel resumed targeting militants after the suicide bombing and a sharp increase in the number of missile attacks launched by Palestinian militants.