Colonel Awni Matar, senior Palestinian security officer in Bethlehem, and Israeli commander General Nissan Alloun led the talks at Israel's military headquarters in the Gush Etzion settlement bloc, west of Bethlehem.
During the meeting, a Palestinian demand that Israeli troops withdraw from all villages and dismantle all checkpoints in the Bethlehem district met with Israeli refusal, the sources added.
A senior Israeli official quoted by public radio said that Israel would not relinquish control over certain areas, notably to the east of the town and around the so-called Tunnels Road northeast of Bethlehem.
An Israeli military spokeswoman confirmed only that a "coordination meeting" took place and that both sides would meet again in coming days.
At a summit with Palestinian leader Mahmoud Abbas on 21 June, Israeli Prime Minister Ariel Sharon agreed in principle to transfer security control of Bethlehem and Qalqilya, if the Palestinians clamped down on "militants".
Israel handed over responsibility for Jericho on 16 March and the northern West Bank town of Tulkarem on 21 March, in line with pledges made at a peace summit held in Egypt in February.
But in early May it froze all fresh transfers until the Palestinian Authority took action against armed resistance groups.
Around 1000 unemployed Palestinians staged a demonstration on Monday in Ram Allah in the West Bank to demand the Palestinian Authority do more to combat poverty in the occupied territories.
The protestors from across the West Bank, gathered outside the Ram Allah offices of Prime Minister Ahmad Qureia after marching through the city's streets.
Palestinians ask their government
for better living conditions
Some demonstrators wore headbands reading "poverty is the enemy of humanity", as others brought along their children to highlight their plight.
Qureia came out to meet the crowd assuring them his administration was doing its best to fight poverty in the Palestinian territories, which he said was caused by the Israeli occupation.
According to official statistics, the rate of unemployment in the Palestinian territories stands at 26% of the working population, with 62% of Palestinian families living under the poverty line.