Canada will restart official talks with the United States on Tuesday in the hope that an updated version of the North American Free Trade Agreement (NAFTA) will be signed off in the coming days.

Canadian Foreign Minister Chrystia Freeland is in Washington to continue negotiations, following the news that Mexico and the U.S. have already reached an agreement that rewrites the trilateral trade pact, first ratified in 1994.

That agreement has been hailed by President Donald Trump as "a big day for trade," sending U.S. stocks to fresh all-time highs Monday, with Asian equities also propelling higher Tuesday.

Maryscott Greenwood, CEO of the Canadian American Business Council (CABC), told CNBC on Tuesday that she thought Canada would join the arrangement and could even finalize a new NAFTA deal this week.

"There is only a handful of tough issues left. Mexico is already there. I think we can get there this week, I really do," she said, before cautioning that this week's trilateral talks would be "harsh" and "intensive."

Later Tuesday, Treasury Secretary Steven Mnuchin told CNBC that he remained hopeful that a revamped trade deal will soon proceed with Canada onboard — but cautioned that the U.S. is ready to go ahead with what it has negotiated with Mexico.

"This is a great move forward for trade," Mnuchin told CNBC's "Squawk Box," a day after the White House announced that it had reached an agreement with Mexico. "I think our objective is to try to get Canada on board quickly," he added.