The invitation appeared to spur the right-wing Likud Prime Minister, Benjamin Netanyahu into meeting Mr Arafat as well.
Last night, Israeli radio announced: "As of now, President Weizman, Prime Minister Netanyahu and Defence Minister Yitzhak Mordechai will meet within two weeks with Yasser Arafat."
Since his election in June, the Prime Minister has prevaricated over setting a date for a meeting with the PLO leader.
A spokesman for the President told The Independent last night that the meeting with Mr Weizman would take place before the Jewish new year, which is on 14 September. Asked whether Mr Weizman would co-ordinate the arrangements with the Prime Minister, he replied: "Maybe, maybe not."
Mr Weizman's initiative places the spotlight on a growing anxiety in Israel's defence, political and media establishment that the Netanyahu government is playing for time and no longer sees a need to maintain the peace momentum. Israelis who had begun to enjoy a more open Middle East suddenly are feeling isolated.
Gideon Ezra, a Likud backbencher and former deputy chief of the Shin Bet internal security service, said yesterday: "It is time to stop playing games with the Palestinians."
The daily Ha'aretz this weekend quoted one senior security official that foot-dragging could provoke renewed attacks by Islamist fanatics. Mr Arafat was coming under increasing pressure, the official said, because of the diplomatic stagnation, the collapse of the Palestinian economy and the violation of human rights by the Palestinian police. "If his distress continues," he added, "Arafat may allow his security forces to ease up on Hamas, and he won't care if there are terror attacks."
After a hastily arranged tete-a-tete with the Prime Minister yesterday, President Weizman denied he had threatened to receive Mr Arafat this week if Mr Netanyahu did not agree to talk to PLO leader within 10 days. He also denied he was trying to take over the negotiations. But the 72- year-old President, who has been a minister under both Likud and Labour colours, was clearly in no mood to accept a prime ministerial veto, or to wait long. Mr Weizman said he had received a letter from Mr Arafat complaining about the stalled peace process. "He is in distress," the President said. "Arafat, whether we want it or not, today has control over two million people. When a leader like this asks to see me, I think I must respond to him."
Despite the unconfirmed report on Israel radio that Mr Netanyahu would meet Mr Arafat, the Prime Minister was still stonewalling. "I don't think it is worthwhile," he insisted, "to hold a meeting that is just ceremonial. When the time comes when I think there will be a purposeful meeting, it will indeed take place."
The Hebrew press, which has never been friendly to Mr Netanyahu, has become universally hostile. Yoel Marcus, Ha'aretz's widely read columnist, detected a reversion to hard-line Likud ideology, which he feared would lead to armed struggles with Palestinians and Syrians. "When the voice is the voice of Netanyahu's pragmatism," he wrote, "but the hands are the hands of a Likud ideologue, the confrontation is written on the wall." His colleague, Zvi Barel, added: "Netanyahu's government is returning Israel to the familiar situation in which it functions best: a small nation surrounded by enemies."