"Lahud calls on the sides ... to live up to their historic responsibilities to protect the higher interests of Lebanon at this sensitive stage by opening an immediate and direct dialogue to lay out all the outstanding problems and reach a consensus in the interest of Lebanon," a statement from Lahud's office said on Saturday.
"The president affirms the need for such a dialogue meeting starting today in any place they agree on, including the presidential palace, which will keep its doors open."
Lebanon has been gripped by political tensions since the 14 February assassination of former Prime Minister Rafiq al-Hariri in a car bomb many Lebanese blame on Syria.
Another car bomb wounded at least eight people in a Christian suburb of east Beirut early on Saturday, raising fears of a
return to Lebanon's violent past.
Syria has bowed to international demands for a troop withdrawal from Lebanon after street protests sparked by the killing, but demonstrators have called for Lahud to go, too.