The report, which has not been confirmed by the Palestinians, came as a Palestinian civilian was critically wounded in the West Bank town of Ram Allah after clashes broke out between local security forces and Al-Aqsa Martyrs' Brigades members.
"Prime Minister Ariel Sharon called Palestinian Authority chairman Mahmoud Abbas to wish him a speedy recovery and said he looked forward to meeting him at their meeting in Jerusalem on June 21 in order to advance the items on the agenda," a statement from Sharon's office said.
Sharon's telephone call came shortly after Abbas returned to the West Bank from Jordan where he had undergone a routine medical exam.
Although the late Yasser Arafat met several times with top Israeli officials, the meetings never took place in the disputed Holy City. Israel considers the entire city its capital, while the Palestinians want east Jerusalem as capital of their future state.
Sharon and Abbas have met in Jerusalem on a number of occasions, but not since Abbas succeeded Arafat as Palestinian Authority president after January elections. The two men last met at a summit in Egypt on February 8.
President Mahmoud Abbas returned
on Wednesday from Jordan
Abbas, who recently returned from a gruelling world tour, told reporters after his return from Amman that he favoured creating the post of vice president.
"I will make a vice president under me. This issue is important and necessary. We must create this position," Abbas said, adding that he would put the idea before the Palestinian Legislative Council and the cabinet, as well as other governing bodies.
Commenting on his landmark summit with US President Bush last week, Abbas said the Palestinians needed to see promises turn into realities.
"There are many important theoretical results, but we are waiting to see what is implemented on the ground," he said.
"President Bush told me important things about the Gaza withdrawal and said it would not be the last withdrawal," Abbas said.
"He also said there must be a connection between (a withdrawal from) Gaza and (from) the West Bank, and that there must be a connection between the Gaza withdrawal and the roadmap," he said, referring to the Middle East peace blueprint.
In Ram Allah, an off-duty member of the Palestinian security services was critically wounded following a dispute with members the Al-Aqsa Martyrs' Brigades, medics said.
Gunfire echoed around the city centre as more than 100 Palestinian security forces surrounded a building in which a number of fighters were holed up.
Mahmoud Abbas (L) met US
President Bush in the White House
The injured man was said to have got into a dispute with the militants after they allegedly insulted a female member of his family. He called the security forces, who turned up en masse, provoking clashes.
During the confrontation, the man was shot by the gunmen, witnesses said.
The Al-Aqsa Martyrs Brigades is a radical offshoot of the ruling mainstream Fatah party.
Support for pullout wanes
Public support in Israel for the planned withdrawal of all troops and Jewish settlers from Gaza appeared to be flagging on Friday. An opinion poll showed support had dropped from 50% from 60% over the past few months.
The poll, published by the Israeli Maariv daily, said 34% were opposed to the pullout due to start in August, while 12% were undecided.