"We don't have permanent enemies - the United States doesn't," Rice told reporters.
"What we have is a policy that is open to ending conflict and confrontation with any country that is willing to meet us on those terms.
"With Syria and Iran we remain open to better relations, but they must choose co-operation not confrontation with the international community," Rice said.
'Anytime and anywhere'
Speaking of Iran, she said she was willing to "meet my counterpart any place and anytime and anywhere and we can talk about anything" but only if Iran suspends uranium enrichment, which Washington fears is aimed at building a nuclear bomb.
But she hinted there was little chance she would travel to Iran, adding "let's not get ahead of ourselves".
She added that Washington would continue to apply pressure behind its diplomacy, referring to US efforts to obtain a third round of UN Security Council sanctions against Iran.
In her speech, Rice also pointed to the Israeli-Palestinian peace process, which the US reactivated for the first time in seven years.
"In the year to come, the president and I will actively facilitate and support these negotiations," she said.
Her words come as the the administration of George Bush, the US president, moves into its eighth and final year.
Many speculate the administration is seeking to leave a more positive legacy after its first years were marked by confrontation and unilateralism, culminating in Bush's "Axis of Evil" speech and the 2003 invasion of Iraq.