"I am with you, because today you represent a free Georgia, a Georgia that sees its future in Europe and will not give anyone the right to take this future," Zourabichvili said in a video statement.
"This law must be abolished in any form. It should not be sent to the Venice Commission. The Venice Commission knows very well what kind of law is this. I said from the very beginning that I would veto this law, and I will do it."
This law distances Georgia from the European Union and all those who support it violate the country's constitution, she said.
Earlier, the presidential administration reported that Zourabichvili had canceled all meetings in the US and planned to make an appeal to the population of Georgia amid ongoing protests.
A protest rally has been taking place since the morning in front of the parliament building in Tbilisi, with dozens of protesters opposing the adoption of the bill on foreign agents, which was approved in the evening in the first reading.
Footage from the scene has shown rally participants throwing stones and bottles at special forces, which in turn have prompted authorities to respond with water cannons and tear gas. Latest footage from the area documented protesters removing barricades that had been installed at the parliament building.
Earlier, the Georgian parliament received a draft law on the transparency of foreign influence, according to which it is proposed to create in the country a register of non-governmental organizations, media and entities receiving funding from a foreign state.
Representatives of the ruling Georgian Dream party told reporters they intended to support the new bill, and if the president vetoed it, the lawmakers would try to overcome it. Opposition politicians believe that it was a "Russian-style" bill alienating the country from the European Union.