Trump made the remarks during a news conference in NY on Wednesday when he was asked if he had, in fact, snubbed Trudeau.
Lighthizer said the timetable for the new deal was set up so Pena Nieto can approve it before he leaves office on November 30 - an arrangement that's acceptable to Lopez Obrador.
The top US negotiator on Tuesday complained Canada was not making enough concessions in bilateral talks to renew the North American Free Trade Agreement and said time was running out before Washington proceeded with a Mexico-only deal. Markets and business groups are openly fretting about the damage that a collapse could provoke.
President Donald Trump on Monday imposed tariffs on an additional US$200 billion of Chinese goods, prompting swift retaliation from Beijing on US$60 billion in United States products.
Canada is looking for a way to reach a deal Trump can hail as a triumph, MacNaughton said.
Earlier on Wednesday, Trudeau shrugged off US pressure to quickly agree to a deal and indicated it was possible the three member nations might fail to conclude a new pact.
Tim Scott, a Republican senator from SC, said Tuesday he'd prefer Canada be included, and wouldn't say if he'd vote for a bilateral U.S. -Mexico deal.More news: Trump questions Kavanaugh's accuser, claims nominee is under attack
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"We're thinking about taxing cars coming in from Canada", he said.
The chief USA trade negotiator is scheduled to meet with Canadian Foreign Minister Chrystia Freeland on the sidelines of the annual United Nations General Assembly meeting in NY.
"We need a three-way auto agreement", Hinrichs said, noting that the deal struck last month between the United States and Mexico could serve as a basis for a more complete agreement that includes Canada.
USA and Canadian negotiators have spent more than a month trying to resolve remaining differences after Washington sealed a tentative deal with Mexico City which they intend to sign by December 1, when a new government takes office.
Trump's comments came during an explosive press conference that included ramped-up threats to slap new taxes on Canada's auto industry - an industry Trump described as "the motherlode" - if a NAFTA deal isn't struck. He has repeatedly said he is ready to walk away from the talks rather than sign a document he thinks is bad.
If higher tariffs take effect, supply chains will be disrupted and the Bank of Canada will be compelled to cut interest rates, the analysts told Bloomberg.
"If it doesn't happen by the end of the week, we'll just keep working away and trying to get the best deal for Canada", David MacNaughton told a Toronto event arranged by Politico Canada. "We don't like their representative very much".
The official declined to be named because the matter has not yet been made public.