Prime Minister Ehud Olmert told his cabinet on Tuesday he hoped Lebanon would follow Syria in opening talks on peace with Israel, a political source said.
"Just as we started talks with Syria, I would hope it would be possible to start talks with Lebanon," the source quoted Olmert as saying.
Israel and long-time enemy Syria have been holding indirect talks under Turkish auspices and further meetings in Turkey are expected later this week.
The source, who spoke on condition of anonymity because Olmert spoke in a closed meeting, said the prime minister "wasn't asking for talks with Lebanon" but was voicing his hope conditions would emerge to enable negotiations to be held.
Israel fought a 34-day war with Iranian-backed Hezbollah guerrillas in Lebanon in 2006. After that conflict, Israeli leaders made peace overtures toward Lebanon's Western-backed government but no diplomatic breakthrough ensued.
Under a deal mediated last month, Hezbollah agreed to join a Lebanese national unity government in which it is guaranteed effective veto power.
Disclosure of the indirect peace track with Syria coincided with a corruption scandal that has led to demands by Olmert's political allies and foes for his resignation.
A US businessman has testified that he gave the veteran politician $150,000 in cash and loans he said have gone unpaid. Both the New York-based fundraiser and Olmert have denied any wrongdoing. Olmert has pledged to resign if indicted.
(Reporting by Dan Williams, Writing by Jeffrey Heller, Editing by Dominic Evans)