SANA said Syria's Foreign Ministry and the United Nations refugee agency had agreed on the issue during a meeting in Damascus. It did not elaborate.
The White House said U.S. President Donald Trump and Saudi Arabia's King Salman agreed in a telephone call on Sunday to support safe zones in Syria and Yemen.
It was Damascus's first comment on the issue since Trump said on Wednesday he would "absolutely do safe zones in Syria" for refugees fleeing violence in the war-torn country.
According to a document seen by Reuters, Trump is expected to order the Pentagon and State Department to craft a plan for setting up the safe zones, a move that could risk escalation of U.S. military involvement in Syria's conflict.
Rebel backers including Qatar have welcomed Trump's support for safe zones, and Turkey says it is waiting to see the outcome of the U.S. president's pledge.
Creation of safe zones could ratchet up U.S. military involvement in Syria, including increased U.S. air power to enforce "no fly" restrictions and ground forces to protect civilians in those areas.
The document gave no details on what would constitute a safe zone, where they might be set up and who would defend them. Policing them could prove difficult in a war zone dotted with armed groups.
Trump has also not provided details about the proposed safe zones, except to say he would have the Gulf states pay for them.