

President Donald Trump would still like Canada to join the trade deal that the U.S. crafted with Mexico, Commerce Secretary Wilbur Ross told CNBC on Tuesday.

However, the U.S. is moving forward on the bilateral Mexico agreement, Ross said on "Squawk Box."

The United States Trade Representative office "already filed with the Congress the notice regarding the transaction with Mexico," Ross said. He said the details should be made public "very shortly," after the consultation period ends.

Ross said the filing also indicated the U.S. would be "totally happy" if Canada were to get on board and make the deal trilateral, like the one it's replacing, the 1994 North American Free Trade Agreement.

"If they don't, we'll simply go ahead with Mexico," said the Commerce secretary, who before joining the White House made a fortune buying stakes in distressed assets.

Last month, Trump announced the U.S.-Mexico pact, saying it will be called the United States-Mexico Trade Agreement.

The president said at the time he's getting rid of the NAFTA name because it has a "bad connotation" due to the U.S. being "hurt very badly" under it.

Canadian Foreign Minister Chrystia Freeland said Monday she will return to Washington this week to resume trade talks, with time running short to meet a U.S. demand for a deal by Oct. 1.

Trump wants the text of any agreement that includes Canada by then, so outgoing Mexican President Enrique Pena Nieto can sign it before he leaves office.

Canadian officials have said they won't be rushed, given the size of the obstacles. Prime Minister Justin Trudeau has repeatedly said he would not sign an unsatisfactory deal.

— Reuters contributed to this report.