Israeli Prime Minister Ariel Sharon has ordered that all contacts be cut with newly-elected Palestinian leader Mr Mahmoud Abbas until Mr Abbas reins in militants.
Palestinian President Mahmud Abbas at his Ramallah headquarters today
The reported move comes a day after Palestinian militants killed six Israeli civilians in a bombing-and-shooting attack on a Gaza Strip crossing.
Mr Sharon's office had no comment on the reports carried by three Israeli television stations. Earlier, Israel signalled it would delay retaliating for the Gaza crossing ambush and give Mr Abbas a chance to rein in violent groups.
The shooting rampage at the Karni crossing, Gaza's main lifeline, marked the Palestinian militants first major challenge to Mr Abbas, who has spoken out against violence and has said he would try to negotiate a truce.
Three Palestinian gunmen were also killed in the attack, and three armed groups claimed responsibility, including Hamas and the Al Aqsa Martyrs' Brigades with ties to Mr Abbas' ruling Fatah movement.
Israel and the United States have said they would judge Mr Abbas by his actions. However, Israeli Justice Minister Tzipi Livni suggested today that Israel would give Mr Abbas, widely known as Abu Mazen, more time to deal with the militants.
"In order to try to prevent the next attack, we have to try and strengthen Abu Mazen as a leader, based on the assumption that he can control the terror groups," Mr Livni said, adding that Israel would draw the line at endangering its security.
In response, Israel indefinitely closed the crossing, through which goods flow in and out of the fenced-in coastal strip. A second Gaza crossing, for Palestinian travellers, was closed last month, after an attack there killed five Israeli soldiers.
The closures mean Gaza is now largely cut off, and the renewed hardships hit Palestinians just a week before a major Muslim holiday. Many Palestinians, exhausted after more than four years of fighting, are complaining privately about the militants targeting crossings.
Mr 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.