"Both the United States and Syria have a very deep interest... in having a very frank exchange on any differences (and) agreements that we have about the possibilities of peace in this region," he said in the statement.
A summit of Arab leaders last weekend ruled out renewed Palestinian-Israeli peace talks unless the Jewish state halts all settlement building, particularly in annexed Arab east Jerusalem.
"There are things that the United States can do, there are things that Syria can do, there are things that Israel can do, Turkey can do, some are unilateral, some are multilateral," Kerry said.
"But all of us have to work together in order to seize real opportunities."
Obama's administration has pursued a year-long campaign to engage Syria, a former US foe, and energise its thwarted push for a broad Arab-Israeli peace, particularly between Israel and the Palestinians.
Its decision in February to appoint the first US ambassador to Damascus in five years was "evidence that engagement with Syria is a priority at the highest levels of our government," said the former US presidential candidate.
Envoy Robert Ford is still awaiting US confirmation of his new post, but "he will be an excellent representative of the president's policies and an outstanding envoy to the Syrian government," Kerry said.
He also called on Syria to play a role to halt the supply of weapons to Lebanon's Shiite militant group Hezbollah.
"We also remain deeply concerned about the flow of weapons in this area, through this area, to Hezbollah. That is something that must stop in order to promote regional stability and security," Kerry said.
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