Israeli officials told Reuters news agency that Israeli Prime Minister Ariel Sharon allowed the meeting to take place on the condition it did not deal with peace issues.
One of the items discussed at the meeting was an international project to collect funds for the Palestinian people, officials from Mr Peres' office said.
A spokesman for Mr Peres, Yoram Dori, said that the meeting would be "the first of a series" and that the Israeli foreign minister would hold talks with other Palestinian officials, including Palestinian Interior Minister Abdel Razaq al-Yahia on Tuesday.
Palestinian Cabinet Secretary Ahmed Abdul Rahman played down the importance of such talks, arguing that it was another attempt by Israel to dictate policy to the Palestinians.
Diplomacy
Since violence began 21 months ago meetings between the two sides have been rare.
But last month Mr Peres received permission to talk to members of Palestinian leader Yasser Arafat's newly reshuffled cabinet, including Mr al-Yahia and Mr Fayed.
The meeting came as the US State Department announced that a high level meeting on the Middle East is likely to take place next Monday.
Spokesman Richard Boucher said the meeting would be held in New York and would consist of the so called Madrid Quartet - comprised of the US secretary of state, the Russian foreign minister, the UN secretary general, and an EU foreign affairs envoy.
Arrests continue
In West Bank cities on Monday Israeli forces temporarily lifted a curfew for several hours, as more suspected militants were rounded up as part of Operation Determined Path, launched on 19 June to combat suicide bombing attacks instigated by groups such as Hamas.
During the curfew break several thousand Palestinians in Qalqilya took to the streets for the funeral of a 9-year-old boy.
He died from critical head injuries sustained when Israeli soldiers fired on Palestinians who had violated the curfew.
Arafat pressure
Addressing a news conference on Monday, President Bush said he believed progress is being made towards the reforms of the Palestinian Authority that he has demanded.
Largely in response to US criticism, Mr Arafat has set about purging and re-organising his security apparatus.
He has already reshuffled his cabinet and called presidential elections for January next year.
However not all of his actions have proved popular with the Palestinian population, with his decision to sack the head of the Palestinian preventative security force in the West Bank, Jibril Rajoub, sparking off protests in several Palestinian towns.
Nonetheless Mr Arafat is still widely expected to win next year's elections.