Washington and Paris had hoped the 15-member U.N. Security Council would vote on the resolution on Monday, but now it appears the vote may come later in the week.
Meanwhile, Israeli airstrikes and artillery pounded parts of southern Lebanon on Tuesday in an effort to cripple Hezbollah strongholds. And Hezbollah fired at least 90 rockets into northern Israel.
Lebanon has offered to deploy 15,000 troops to the south to support a peacekeeping mission and to rein in Hezbollah militants.
Lebanese Prime Minister Fuad Saniora praised Hezbollah's resistance, but said it was time for Lebanon to "impose its full control, authority and presence" over the war-weary nation, according to the Associated Press.
Israeli Prime Minister Ehud Olmert called the troop deployment "interesting" and said Israel would favor pulling out once Hezbollah was no longer a direct threat, reported the AP.
Diplomats say they are waiting to hear from three Arab League officials -- the foreign ministers of Qatar and the United Arab Emirates and Arab League Secretary-General Amr Moussa -- before voting on the measure.
Arab ministers, who met in Beirut on Monday, said the resolution appears to favor Israel.
U.N. Ambassador Vitaly Churkin of Russia said his country's support would hinge on Lebanon's view of the final draft, according to Reuters. Russia has the ability to veto the resolution.
Lebanon is seeking the rapid withdrawal of 10,000 Israeli troops in Lebanon after a truce is declared.
Israel is refusing to leave until an international force arrives and the two soldiers abducted by Hezbollah on July 12 are released. The abduction of the troops triggered the intense fighting between the two groups, which has led to the deaths of at least 965 Lebanese and 100 Israelis, Reuters reported.