Fouad Siniora said Israel must leave the Shebaa Farms border area so his government could have authority over all its land and he asked the US president to help achieve this goal.
"Israel should withdraw from all the territories that belong to Lebanon. This would be a very important step in the process we are taking so that we reach a point where Lebanon will be liberated from all Israeli occupation," Siniora said at the National Press Club in Washington.
Siniora, who discussed the issue with Bush this week, said Bush listened carefully and voiced "appreciation for our request".
Israel took control of the tiny region where Israel, Syria and Lebanon met during the 1967 Middle East War. The United Nations and Israel say Shebaa is Syrian land, but Lebanon argues it belongs to them.
Asked whether the United States would put pressure on Israel over Shebaa Farms, Sean McCormack, the State Department spokesman, said the disputed territory was an issue for Syria and Lebanon to work out.
He said public statements from Syria and Lebanon indicated agreement that the disputed territory belonged to Lebanon but Syria was not prepared to enter negotiations on this.
"Syria is all too happy to let the situation stand as it is, because in their view, there is no percentage in beginning a negotiation with Lebanon on this," said McCormack.
Israel took control of the Shebba
Farms in the 1967 war
"So I think it is a fair assessment to say that they are the key stumbling block to resolving these issues."
Lebanon says Israel's 2000 pull out from southern Lebanon was incomplete, a claim that has allowed Hizbollah guerrillas to continue to launch sporadic attacks on Israeli forces from there.
In a report on Tuesday, Kofi Annan, the UN secretary general, said Lebanon must set its borders with Syria and disband Hizbollah, a Shia Muslim group supported by Syria and Iran, before it could be master of its own nation.
In turn, Annan said Syria should take up Lebanon's offer of establishing diplomatic relations as well as demarcating the entire 250km (160-mile) boundary between the two countries.
Syria has said it is premature to establish diplomatic ties with Beirut and has refused to demarcate the border.
Syria withdrew its forces from Lebanon a year ago after protests over the assassination of Rafik Hariri, former Lebanese prime minister.