Lebanon hopes Monday's unanimous decision by the government, which includes two Hezbollah ministers, could pave the way for changes to a UN Security Council resolution to end 27 days of Israeli and Hezbollah attacks.
The Lebanese army has called up reservists ahead of the planned deployment to the south, where thousands of Israeli troops are clashing with Hezbollah fighters.
The Lebanese military has a standing force of about 60,000 troops.
The measure was announced by Ghazi Aridi, the Lebanese information minister, after an extraordinary cabinet meeting.
"The government stresses its willingness to send a 15,000-strong Lebanese army force to deploy in south Lebanon as Israeli forces pull back behind the Blue Line (border)," the cabinet said in a statement read by Aridi.
The statement also said the army was willing to seek the help of a strengthened UN peacekeeping force in Lebanon.
Aridi did not explicitly say whether Hezbollah would pull out from border areas, adding that he would not reveal any future steps.
However, he did say the army would be "alone" in the south.
Aridi added that the Lebanese army is ready to accept help from the United Nations Interim Force in Lebanon that has 2,000 peacekeepers in south Lebanon.
Opposition to UN draft
Fouad Siniora, the Lebanese prime minister, has called again for a ceasefire.
Lebanon says it is unhappy with a US-French draft resolution to end the fighting, demanding that it include a call for the immediate withdrawal of Israel's 10,000 troops from southern Lebanon.
Lebanon's opposition has caused the US and France to delay a vote on the resolution.
While Israel has not formally commented on the draft resolution, one senior government official and Israeli media have said the government views it favourably, partly because it would allow soldiers to remain in southern Lebanon until an international force arrives to take over.