Palestinian Authority President Mahmoud Abbas and Israeli Prime Minister Ehud Olmert have held talks in Jerusalem.
Mr Abbas was introduced to Mr Olmert's wife, Aliza
The meeting, at Mr Olmert's residence in the city, lasted nearly two hours.
The pair met informally in June, but these were the first formal talks between Israeli and Palestinian leaders for nearly two years.
It comes after a recent truce following months of fighting in the Gaza Strip after the capture of an Israeli soldier by Palestinian militants in June.
Mr Abbas was greeted by the Israeli leader as he arrived for the meeting. The two men shook hands and kissed each other on the cheek, then Mr Olmert introduced his guest to his wife Aliza before they sat down to talk.
The BBC's Katya Adler in Jerusalem says the private meeting, which follows months of preparation work by Israeli and Palestinian officials, cannot be described as peace talks - rather an attempt to establish some confidence-building measures.
According to Palestinian negotiator Saeb Erekat, Mr Olmert agreed to release $100m in tax money which Israel collected on the Palestinian Authority's behalf, but which it had refused to transfer since Hamas formed a government in March.
No agreement was made over the release of thousands of prisoners held in Israeli jails, although both sides agreed to set up a committee to discuss the issue.
Israel has said before that it will not consider any releases unless the captured soldier, Gilad Shalit, is released first.
Hamas sticking point
Mr Olmert did however agree to ease travel restrictions on Palestinians and remove a number of checkpoints in the West Bank.
"This is the beginning of a series of meetings. It was a good meeting. There was agreement on several issues," Palestinian official Nabil Abu Rdainah told Reuters news agency after the meeting.
Mr Abbas and Mr Olmert have both said recently that they want to re-start peace talks, but both sides have also played down the prospects for any rapid progress.
It is thought Israeli soldier Gilad Shalit is still being held in Gaza
Israel has repeatedly said it will not deal with the Hamas-led Palestinian government, which refuses to recognise the legitimacy of the Jewish state.
Mr Abbas says his attempts to persuade Hamas to change its position have failed. Last week he called for early elections, but Hamas denounced this as a coup attempt.
The dispute led to some of the worst factional fighting between Palestinians in years, prompting fears that the violence was descending into all-out civil war.
Israel has been under pressure from the US and the European Union in recent days to take steps to support Mr Abbas, our correspondent says.
Correspondents say a breakthrough in the stalled Middle East peace process would help both leaders, with Mr Abbas suffering from the conflict with Hamas, and Mr Olmert losing popularity in Israel over his handling of the war with Lebanon this summer.