He said the U.S.is "very unhappy with the negotiations and the negotiating style of Canada".
Trump's new threat came four days before the U.S. -imposed deadline of September 30 for Canada to provide the U.S. Congress with an updated text of the North American Free Trade Agreement (NAFTA) deal.
While some lawmakers have ratcheted up pressure on Canada to sign, others such as Nancy Pelosi have said the Trump administration should reach a trilateral deal.
Canada needs a NAFTA deal "that involves obviously feeling confident about the path forward", the prime minister said.
Trudeau also downplayed a brief handshake with Trump at a luncheon Tuesday, where the US president remained seated despite standing to greet other leaders.
Speaking at the United Nations General Assembly on Tuesday, Trump touted the success of his trade policy, citing the renegotiated bilateral trade deal with South Korea, as well as a partial rework of NAFTA agreed to with Mexico.
Auto tariffs in particular "would change the whole relationship for a long time come", he added.
Lighthizer said Tuesday that the administration will immediately submit the text of a U.S. -Mexico deal to Congress if Canada does not sign on by then.
"I'm not going to use the name 'NAFTA, '" he said.
"We're thinking about taxing cars coming in from Canada", he said.
Mexico and the United States announced a bilateral agreement on August 27, leaving Canada out of the rewrite of the 24-year-old deal that set up a regional trading zone.
"We'll see where it goes, but so far it's been tough", he said.
The deal, if enacted, would not be almost as disruptive as what Trump has long threatened, to get rid of NAFTA, which he claimed had cost thousands of auto industry jobs. If Canada comes along now, that would be the best.
Trudeau said existing USA tariffs on Canadian steel and aluminum in late May would have to be scrapped before Canada felt comfortable signing a new NAFTA.
Ford Chief Executive Officer Jim Hackett said Wednesday that the Trump administration's tariffs on imported steel and aluminum will cost the company $1 billion.
Mexico's negotiators convinced Washington to drop a demand for curbs on seasonal food imports and to retain an exemption granted under NAFTA from industrial tariffs imposed by the United States under World Trade Organization (WTO) rules. Supporters of Mexico's incoming government, which takes office December 1, are not especially fond of NAFTA, which is why both countries want the deal done before then. "We don't have any comment beyond that".