"Two suicide bombers attacked Marjeh square causing casualties and material damage," the broadcaster said.
The channel screened images showing badly damaged vehicles and bloodied pavements.
"It seems the terrorists have struck again," said a television presenter, using the regime's term to refer to rebels fighting President Bashar al-Assad's troops.
The Syrian Observatory for Human Rights also reported the blasts, but said they were caused by explosive devices planted in the neighbourhood.
"Several people were wounded by two explosive device blasts in Marjeh square in Damascus," said the Britain-based Observatory, which relies on a broad network of activists, doctors and lawyers for its reports.