Scores of others among the more than 1,000 demonstrators were wounded, The Washington Post reported.
The gunfire erupted after security forces blocked the path of the demonstrators, who seek the ouster of President Ali Abdullah Saleh. Protesters ran when the gunfire, accompanied by tear gas, began and some were trampled in the chaos, the newspaper said.
Abdul Malik al-Ansi, a doctor at the field hospital at "Change Square," told the Post 13 people had died and more than 50 had been shot. Others there said they expected the toll to increase.
"They shot at us with .50-caliber machine guns, with AK-47's, with everything," human rights activist Khalid al-Ansi told the Post. "I don't know how many are dead, but there must be scores."
Wednesday's clash was the most violent since at least 52 people died in a March 18 protest.
The protest leaders had issued a nationwide call for the rally, Kuwait's KUNA news agency reported.
The statement warned against accepting the initiative of the Gulf Cooperation Council that would grant Saleh and his aides immunity against future prosecution.
Thousands of Yemenis took to the streets in several cities Tuesday to protest the killing by security forces of seven demonstrators and the injury of hundreds of others in the central city of Ta'iz and Al-Hudayah in western Yemen.
They accused Saleh of dragging the country into civil war.