But the White House said in a statement it is "not currently in a position to join the endorsement".
"We continue to be proactive in our efforts to counter terrorist content online while also continuing to respect freedom of expression and freedom of the press."
Smith said he "would have loved" the US Government to sign up and expected that more countries and tech companies would sign on in the coming months.
"We'll continue to encourage the US Government to support this in a variety of different ways."
Prime Minister Jacinda Ardern noted that the Call to Action preserved the principles of legitimate free speech.
Given that, she would not say whether the US had anything to fear from signing up.
"Ultimately that was a decision for them. The fact they took the step of putting out a supportive statement does speak volumes.
"The very fact that, given a lot of the call puts the onus on tech companies, their presence I really saw as being critical.
"Contact with the US will be ongoing. It has been to date and that will continue."
Ardern wrapped up the French leg of her trip this morning with a bilateral meeting with Canadian Prime Minister Justin Trudeau.
Trudeau paid tribute to Ardern and her leadership on the Christchurch Call to Action, which Canada has signed.
Trudeau said it would commit "to a positive path forward to counter radicalisation and bring people together".
Radicalisation is not expressly mentioned in the Call to Action, but it is part of the broader issue of preventing social media users from being sucked into the algorithmic rabbit holes that can lead to extreme views.
"Your leadership following Christchurch resonated around the world ... I really want to thank you for that," Trudeau said.
"There's a lot more to do, but having the tech companies in this conversation is already a first important step."
Ardern thanked Canada for taking the time to travel to Paris to sign the call, and echoed French President Emmanuel Macron's comments that the support of Canada was important given the fact that the United States had not signed.
"The presence of Canada was really meaningful," Ardern said.
"Those expressions of freedom of speech can live in harmony with what we are tying to do with the work against violent extremism and terrorism."
Ardern has a quick stopover in Singapore for a bilateral meeting with Prime Minister Lee Hsien Loong before heading back to New Zealand.
"The focus for us will be the trade relationship."