The Israeli and Palestinian leaders have held talks in
The meetings were at Prime Minister Ehud Olmert's office, involving teams of negotiators before one-on-one talks.
The leaders did not issue statements after the talks, meant to pave the way for an international peace conference.
Israel has backed Mr Abbas since his Islamist rivals Hamas seized control of Gaza in June, but made few concessions.
Israeli sources told the BBC Tuesday's meeting discussed security issues which could lead to the lifting of some travel restrictions in the Israeli-occupied West Bank and addressed the issue of arms smuggling into
Earlier Israeli officials said a declaration of principles and understandings discussed at Tuesday's meeting would be kept vague, but Mr Abbas has urged they deal with substantive issues.
On Monday, he said that an international peace conference hosted by the
Israeli officials had said Mr Olmert had planned to express his appreciation for the Palestinian security forces, which rescued an Israeli army officer who accidentally entered the West Bank town of
After Hamas's victory in
PHOTO CAPTION
Israeli Prime Minister Ehud Olmert