"We want the government to reflect Lebanese consensus and the (terms) of the Doha accord, and I will strive to do that in the next few days," he said.
Siniora was reappointed on Wednesday by Sleiman and asked to form a new cabinet.
Earlier in the day, a Lebanese soldier was killed by an explosion in the north of the country, the military said, without identifying the cause of the blast.
A military statement identified the victim as Osama Ahmed Hassan, 24.
A security official said the explosion occurred at 5am local time (0200 GMT) in the Abdeh area near the northern outskirts of Ain al-Hilwah, a Palestinian refugee camp.
Man shot dead
An army spokesman later said that soldiers shot dead a man carrying a hand grenade outside Ain al-Hilwah.
"The man was carrying a hand grenade and we are also investigating whether the belt he was wearing contained an explosives charge," he said.
The spokesman refused to provide any further details.
Earlier, security officials said that the army had found another device inside the post primed and ready to detonate but that explosives experts defused it before it went off.
Investigators are trying to determine when the explosives were planted, the official said.
Saturday's blast came a year after the Lebanese army was involved in deadly battles with armed groups in the Nahr al-Bared Palestinian refugee camp just north of Tripoli.
More than 400 people were killed, including 168 soldiers, in more than three months of fighting which ended in September 2007.