Israeli leaders said they made no distinction between Lebanon and Hezbollah now that the Shiite movement was part of the government.
The comments came amid growing tensions along the border between Israel and Lebanon. Beirut filed several complaints with the United Nations saying that Israel was violating its national sovereignty, while Jerusalem said recent Hezbollah activity along the border is a sign of a pending strike.
Suleiman responded by saying the latest threats from Israel should encourage lawmakers to form a new government to counter the tensions.
"The recent barrage of Israeli threats, which show the enemy's hidden intentions toward Lebanon, calls on us to work hard to strengthen and close our ranks," he said.
Meanwhile, Abdul Amir Qabalan, Lebanon's highest Shiite authority, lashed out as Israel for its "blatant interference" in Lebanese affairs, Hezbollah's al-Manar news service reports.
"Israel awaits us at the doors," he said. "This is why you (political leaderships) must reach an agreement and form a government as soon as possible."
Prime Minister-designate Saad Hariri has struggled to form a national unity government following the victory for his March 14 coalition over the opposition March 8 slate in June parliamentary elections.