The United States, Mexico and Canada have been bogged down in trade negotiations for the past nine months, with progress held up by U.S. demands to impose tougher minimum content requirements for autos built in the region.

For a deal to be struck to rework the 24-year-old accord, U.S. negotiators would need to show flexibility, Guajardo said.

"I think there's a 40 percent probability of being able to conclude it before (July 1)," he told Mexican television.

If not, there was about an 80 percent chance of finishing the renegotiation before the U.S. mid-term congressional elections in November, Guajardo added.

U.S. President Donald Trump wants to change the auto rules to create more manufacturing jobs in the United States. He blames lower-cost Mexico for the loss of U.S. employment.

Guajardo said it was important to agree a new NAFTA deal as quickly as possible, but not at the expense of quality.

On Thursday, Mexican President Enrique Pena Nieto expressed optimism about the process after a phone call with Canadian Prime Minister Justin Trudeau. Still, talks were complicated this week by a U.S. probe looking at auto tariffs.

Canada's government said that during the call, the two discussed their "strong concerns" about the so-called Section 232 investigation by the United States into whether imports from around the world were harming the U.S. automobile industry.

Guajardo said talks should not be distracted by the U.S. probe, which he noted had been lampooned in the United States, describing the initiative as a "fireworks display."

Mexico has proposed that 70 percent of overall content of a vehicle made in North America come from the region, countering a U.S. proposal of 75 percent for high-value parts.

The United States also wants 40 percent of auto content to be sourced from areas paying at least $16 hour. Mexico has proposed that 20 percent of any auto made in the region be from high-wage areas, an industry source briefed on it said.

Guajardo also denied there was a rift between him and Foreign Minister Luis Videgaray over the NAFTA talks. He was responding to media reports that Videgaray was pushing for a quick deal, while he was holding out for a better one.

Guajardo also addressed suggestions by the front runner in the presidential election, leftist Andres Manuel Lopez Obrador, that the NAFTA negotiation should be postponed until the next Mexican government takes office in December.

In reality, whoever was the next president did not want to have to take office faced with NAFTA, he said. "Deep down, what they want is for this problem to be taken from them."

(Reporting by Dave Graham; Additional reporting by David Ljunngren in Ottawa; Editing by Nick Zieminski and Susan Thomas)

By Dave Graham