The announcement by the two prominent Palestinian factions came after talks with the Palestinian Authority (PA) President Mahmud Abbas on Saturday.
"Hamas is going to maintain its cooling down period," Hamas leader Ismail Haniya said.
Islamic Jihad leader Muhammad al-Hindi also made a similar commitment after meeting Abbas.
The Palestinian president had been seeking the two groups' agreement to a mutual ceasefire with Israel, which he announced at a summit with Israeli Prime Minister Ariel Sharon in Egypt on Tuesday.
Walid al-Umari, Aljazeera's correspondent reporting from Ram Allah, said Hamas and Islamic Jihad had confirmed their commitment to maintaining a temporary calm, adding that if Israel violated the ceasefire, the resistance movements would first notify the PA before responding.
They have also announced their conditions to this temporary ceasefire, stating that they are waiting to see how truthful Israel is in implementing any of the agreements, especially the ceasefire, al-Umari said.
The resistance movements have expressed scepticism at Israel's commitment and drew parallels to the time when Abbas was Prime Minister during Arafat's era, where Israel violated the agreements.
The announcement indicates that the resistance movements want to be certain that Israeli military operations against Palestinians will come to a halt, as agreed upon at Sharm al-Shaikh summit, the Aljazeera correspondent said.
Islamic Jihad leaders have
accepted a temporary truce
Keen to cement a ceasefire, Abbas had sacked three senior security officials in the Gaza Strip after they failed to stop Hamas fighters from firing mortars into Israel on Thursday.
The mortars were in response to the killing of two Palestinian men, Hasan al-Alami and Fathi Abu Jazzar.
Aljazeera correspondent also summarised some of the confidence-building measures to be implemented this week.
They include the handover of certain areas to the PA, the release of detainees and the handing over of Palestinian fighters' remains.
"Hamas is going to maintain its cooling
Israel will first handover Jericho to the PA, followed by Qalqilya or Tulkaram, he said.
Israel is also supposed to release about 900 Palestinian detainees and hand over the bodies of 15 Palestinians currently in Israel's custody.
Palestinian Authority officials including Mahmud Dahlan and Israel's minister of defence, Shaul Mofaz, met on Saturday evening and a follow-up meeting is planned for Sunday where security coordination is to be discussed, al-Umari said.