A leading U.S. Republican senator on Tuesday urged allies Australia and Japan to continue to move forward with the Trans-Pacific Partnership free trade negotiations, despite the U.S. withdrawal,

"I know Australia is now talking with Japan and others about moving forward with TPP despite America's withdrawal. I would strongly encourage that," Sen. John McCain said in a speech in Sydney.

"The case for an open, rules-based, regional economic architecture is just as compelling today as it ever was. So I would urge you to keep at it. And hopefully, someday in the future, under different circumstances, America will decide to join you," he said.