Clinton said the violent protests of the past two weeks in the Arab Spring states "exposed deep rifts within new democracies and volatility that extremists were quick to instigate and exploit."
Reiterating President Obama's stance before the U.N. General Assembly a day earlier, Clinton said "the United States rejects the false choice between democracy and stability."
"Democracies make the strongest, most capable partners. And we know that it takes a lot of hard work and oftentimes struggle," she said. "But the fact of new, emerging democracies here in the 21st century should be a cause for great satisfaction and hope. But these emerging democracies need champions, not fair-weather friends."
The United States' top diplomat said she told leaders in Tunisia, Libya, Egypt and Yemen they have America's "unwavering support" in their "continued journey along the democratic path."
She said international support will be critical in their success.
In Syria, she said, "we continue to insist that the violence must end and a political transition without [President Bashar] Assad must move forward."
Though pressure from the Arab League and many other nations has been exerted on the Assad regime, the civil war there has continued unabated.
"I would urge that we try, once again, to find a path forward that can bring the Security Council together on the urgent business of both ending the violence in Syria and preventing the consequences that all of us around this table fear," she said.
Clinton also put in a plug for efforts to push forward the Israeli-Palestinian peace process and to rein in Iran's nuclear ambitions.