Peres: No mandate to negotiate
Prime Minister Guy Verhofstadt, who holds the EU's rotating presidency, invited Mr Peres and Mr Arafat after holding separate talks with them earlier in the day. No statements were made after the meeting.
Monday's meeting came as a 16-year-old, killed on Sunday by a Palestinian gunman in an attack on a bus, was buried in the Jewish West Bank settlement of Betar Illit.
Mr Peres, who is in Brussels attending a conference of European Union and Mediterranean countries, has said he has no mandate to negotiate with Mr Arafat until he outlaws Muslim militant groups.
"The main crisis is not one of rhetoric but of action," he told a joint news conference with the Belgian Prime Minister.
"The real problem is one of credibility. What was promised was not realised. We are looking for real action," Mr Peres said.
Mr Verhofstadt said it was "unrealistic to think that in a few hours or days it is possible to have a long period of no violence, but we have to try."
Israeli withdrawal
The Israeli foreign minister said it was hard to sit with Mr Arafat after Sunday's attack, in which two teenagers were killed and about 50 people were injured.
Despite the shootings, Israel completed its withdrawal from the town of Qalqilya in the West Bank - one of six areas it occupied after the assassination of an Israeli cabinet minister last month.
Israel has been under intense pressure from its key ally, the US, to pull out of the West Bank towns, for fear that heightened tension in the area could jeopardise the American-led coalition against international terrorism.
Israeli forces last week pulled out of Bethlehem and nearby Beit Jala, two other towns they occupied after the assassination of Tourism Minister Rehavam Zeevi.
Ongoing violence
Two Palestinians were wounded in a shootout with Israeli troops in the Palestinian-controlled town of Rafah in the Gaza Strip on Monday.
The clash came after Israeli forces demolished two buildings in the area, Israel Radio reported.
In Sunday's attack in Jerusalem, a Palestinian gunman opened fire on a bus at the French Hill junction in the north of the city.
A border police officer and a soldier shot and killed the gunman, Jerusalem police chief Mickey Levy told Israel radio.
Mr Levy identified the attacker as a member of the militant group Islamic Jihad, from the West Bank town of Hebron.
In a statement, the Palestinian Authority "strongly" condemned the shooting and vowed to bring the guilty parties to justice.
But the statement also blamed Israel for "the deterioration of the situation... due to its continuing occupation of Palestinian autonomous areas and its policy of assassinating Palestinians."
Diplomatic pressure
Israeli sources have told the BBC there is no timetable to leave the remaining three towns of Ramallah, Tulkarm and Jenin.
The United States has been pushing Israel to resume talks with the Palestinians and pull out of the towns it has occupied in the West Bank.
Israeli Prime Minister Ariel Sharon has said his forces will only withdraw when the Palestinian Authority has outlawed militant groups and handed over those responsible for Mr Zeevi's assassination.