The meeting at Erez, just outside the Palestinian autonomous enclave in Gaza, was notably warm, in contrast with the confrontational atmosphere at summits between Mr Arafat and Benjamin Netanyahu, the former Israeli premier.
In a series of meetings with Arab leaders and US President Bill Clinton last week, Mr Barak showed he wanted to reach peace agreements while he still has the momentum of his May election victory.
Mr Arafat described the latest meeting as "constructive, fruitful and productive". Mr Barak said that "both sides had suffered enough".
Before the talks opened, the leaders exchanged gifts and, at one point, Mr Barak helped Mr Arafat, who is in poor health, on to the podium.
Mr Barak promised to implement the Wye land-for-security deal signed by his predecessor, which the Palestinians want to see fulfilled as a sign of good faith. "We are committed to the Wye agreement," he said. But he added that Israel wanted to co-ordinate the implementation of the accord with final talks on other issues such as Jerusalem, refugees, borders and Israeli settlements.
The difficulty for Mr Barak is that implementing the Wye deal might lead to a confrontation with Israeli settlers. Israel would prefer to start with opening a "safe passage" between the Palestinian-controlled West Bank and the enclave of Gaza, a release of Palestinian prisoners and the opening of a Palestinian port at Gaza.
Mr Barak repeated his position on Israeli settlements, saying he would not start new ones or close down ones that existed already. He also said he would reconsider any decisions taken by the last government but not yet implemented. This could affect the status of new settlement plans announced in the last months of Mr Netanyahu's government.
The Israeli leader later told Israeli television that he wanted two months before implementing any agreements. Nevertheless, Palestinian leaders appear impressed by the speed with which Mr Barak is moving to resuscitate the peace negotiations.
Mr Barak is to see King Abdullah of Jordan in Aqaba today before a six-day visit to the US, where he will meet President Clinton. This may worry Mr Arafat, who does not want to be confronted by a joint US-Israeli position on peace negotiations. The Palestinian leader has recently had much improved relations with Washington because of friction between President Clinton and Mr Netanyahu.
The Palestinians also worry that Mr Barak might give priority to negotiations with Syria about the Golan Heights. The Syrian Times praised the Israeli prime minister at the weekend "for taking an important, positive step towards renewing the discussions where they were halted three years ago". Since a framework for an agreement between Israel and Syria had already been reached, a peace treaty "is possible within a few weeks".
There is growing evidence that Mr Barak wants to move quickly to reach an agreement with Syria and the Palestinians. The Israeli press says the government is prepared to reach a final status deal with the Palestinians within six months. Mr Barak may calculate that drawn-out negotiations would give Israel's nationalist right, currently demoralised by its election defeat, time to rally.
Mr Barak is in a strong position because he is supported by 75 of the Knesset's 120 members. Mr Netanyahu's resignation has also left the right leaderless. Parts of Mr Barak's coalition are opposed to an extensive withdrawal from the West Bank, but he can draw on enough support in the Knesset to make it impossible for any one party to bring him down.