Cabinet minister Saeb Erekat said, "A decision was taken that we will handle our obligation to stop violence against Israelis anywhere."
The order comes one day after Abbas' swearing in and three days after an attack on an Israeli security checkpoint by Palestinian militants that left six dead. Israel responded to that attack by cutting off all communication with Abbas and sending helicopter gunships to strike a Palestinian refugee camp.
U.S. Secretary of State Colin Powell reportedly phoned Abbas over the weekend and urged him to clamp down on the militants.
The Israeli government said through a spokesman Monday that the cabinet's order to stop militant attacks was a "small step in the right direction" that could lead to a re-establishment of communication between the two sides.
After last week's attacks Israeli Prime Minister Ariel Sharon reportedly ordered his military to take action in the Palestinian controlled Gaza Strip in order to "stop terror." News reports on Monday said that Israeli officials have decided to delay action in order to give the Abbas' government a chance to get control over militants.
Abbas was reportedly angered that the Israeli government publicly held him responsible for last week's attacks, which occurred before he had officially taken power.
Attacks by militant groups on Israeli targets have been one of the major points of contention in the Middle East peace process. Abbas has said he intends to rein in militants. One of the main militant groups, the Al Aqsa Martyrs Brigade is associated with Abbas' Fattah political party.
Abbas has said in the past that he would avoid violence in dealing with militants but Prime Minister Ahmed Qurei said Monday that those seeking to carry out attacks would be "punished."
For their part militant groups have said that their attacks are in response to Israeli encroachment on Palestinian land and the killing of civilians by the Israeli military.
Spokesmen for the three main Palestinian militant groups immediately dismissed the cabinet's order.
"We consider resistance as a red line, and no one is allowed to cross this line," Hamas spokesman Mushir al-Masri said.
Islamic Jihad leader Nafez Azzam said the cabinet's move "will not resolve the problem but it could cause a Palestinian-Palestinian problem," but added he hoped "things will be solved through dialogue."
Abu Qusai, a leader of the Al-Aqsa Martyrs said in order for attacks to be prevented "Israel must stop the deliberate and daily killing of Palestinian people."
Abbas is scheduled to travel to the West Bank Tuesday to begin cease-fire negotiations with militant leaders.
Meanwhile violent exchanges continued on Monday, with Israeli soldiers killing two Palestinian gunmen near a Jewish settlement in Gaza and Palestinian militants firing missiles into Israel.