Livni, the former head of Israel's Kadima party, says in a guest editorial published in the Financial Times Thursday Morsi, a former leader of the Muslim Brotherhood, will help determine whether Egypt continues a march toward democracy or turns to radical extremism.
Livni resigned from Israel's Knesset last spring after losing in Kadima party primaries but last month said she is not ending her political career, Ynetnews reported.
"Whether we are facing an Arab Spring or an Islamic winter depends very much on Egypt's president Mohamed Morsi but also on how the international community treats him," she wrote.
Iran has invited Morsi to the Non-Aligned Movement conference in Tehran in August and U.S. President Barack Obama has invited him to Washington.
Livni said while the recent Egyptian elections "strengthen the most radical elements" in the Middle East, Egypt's political realities are too complex to define Morsi as simply an Islamist.
"Whether nor not Islamist groups are impelled to moderate their positions depends to a great extent on the demands made of them by the international community in return for support for their countries," she wrote.
"Without strong Arab backing, it will be hard, if not impossible, for a Palestinian leader to reach peace with Israel."