"Israel informed international leaders today that there will be no meetings with Abbas until he makes a real effort to stop the terror," said Sharon spokesman Assaf Shariv.
Shariv said officials from the U.S., E.U Britain and the Palestinians were notified. Palestinian Cabinet Minister Saeb Erekat confirmed this.
"Sharon's bureau called me this afternoon saying that they were suspending all contact with the Palestinian side," Erekat said.
Shariv said Israel made the decision because the attack on the Gaza crossing was launched from a Palestinian Authority base.
Earlier, Israel had signaled it would hold off on harsh retaliation for the bombing and shooting attack by Palestinian militants, giving the newly-elected Abbas a chance to rein in violent groups.
In quick response to the attack, however, Israel indefinitely closed the Karni crossing and two other main Gaza terminal crossings, through which goods flow in and out of the fenced-in coastal strip. The Erez crossing is also used by journalists, diplomats and some Palestinian workers with jobs in Israel.
Thursday night's shooting rampage at the Karni crossing, Gaza's main lifeline, marked the militants' first major challenge to Abbas, who has spoken out against violence and has said he would try to negotiate a truce.
The terror attack at the Karni crossing and Israeli military operations both "do not benefit the peace process," Palestinian Authority Chairman Mahmoud Abbas told journalists in Ramallah on Friday.
"This attack, as well as Israel's military incursions which killed nine Palestinians this week, do not advance the peace process," he added.
Three Palestinian gunmen were killed in the attack, and three armed groups claimed responsibility, including Hamas and the Al Aqsa Martyrs' Brigades, which has ties to Abbas' ruling Fatah movement.
Palestinian officials said Friday that such attacks are to be expected unless Israel halts its military operations in the West Bank and Gaza Strip.
But the Palestinian Authority also told militant groups that attacks against the border crossings harm innocent Palestinian civilians. The closures prevent the passage not only of Palestinian workers into Israel but also of food, medicine and other supplies into the Palestinian areas.
Israel and the United States have said they would judge Abbas by his actions.
An Israeli Arab member of the parliament, Taleb A-Sanaa, told Israeli Army Radio that Abbas was upset with Israel for holding him responsible for the attacks even though he has not yet been sworn in as the Palestinian Authority chairman.
Abbas has said he will not use force against militants. Instead, he is expected to try to co-opt them by asking Al Aqsa gunmen, many of them former policemen, to return to their jobs, and by offering Hamas a say in decision-making. The Islamic militant group has also said it would participate in legislative elections in July.
In coming weeks, Abbas is to conduct Egyptian-brokered talks with the militants in Gaza and in Cairo. Egypt has renewed a proposal for a one-year suspension of attacks, according to a senior Hamas official, who spoke on condition of anonymity.
Militants are divided on how to respond to Abbas.
Sami Abu Zuhri, a Hamas spokesman, said the attack "was a message to the Israeli enemy, definitely not to Abu Mazen." He said meetings with Abbas would resume soon "to organize the Palestinian house."
The top Hamas official in the West Bank, Hassan Yousef, said the group is ready to suspend attacks as part of a deal with Abbas. Asked about Thursday's attack, Yousef said Hamas had freedom of action as long as there is no agreement.
Iranian-backed Hezbollah guerrillas in Lebanon are emerging as a major spoiler. Hezbollah is funding small groups within the militant factions, including some Al Aqsa gunmen in the West Bank city of Nablus.
Palestinian Cabinet Minister Ghassan Khatib said Abbas wants a mutual cease-fire, including Israeli assurances that it halts its military operations. "He does not say that we have to stop the Palestinian attacks while the Israelis can continue their attacks without any response," Khatib said.
Khatib said he believes the militants want a truce, "and the question now is whether Israel is ready for that or not."
Israeli Transport Minister Meir Shetreet said Abbas' attempt at persuasion would fail and that he must crack down. "There has to be zero tolerance for terrorists," Shetreet told Israel Radio. "If he (Abbas) doesn't do this, he misses a great opportunity to lead the Palestinians in a different direction."
The attack happened just before 11 p.m. Thursday.
, blowing out a large hole in a door in a security wall at the crossing, said Israeli Brig. Gen. Aviv Kochavi, commander in the Gaza division.
Kochavi said the military has been trying to ease restrictions on Palestinian movement, and that the militants "are ruining all of this for their people."
"This is a central crossing through which merchandise, medicine and food are brought," Kochavi told Israel Radio. "For a reason that is not clear to us, [the militants] are making every effort to destroy our every attempt to allow the Palestinians, their own people, [to lead] easier lives."