MEXICO CITY -- One day last month, the presidents of the United States and Mexico held an angry phone call that scuttled a planned meeting between the two leaders. Three days later, President Trump threatened in a tweet that Mexico "must help MORE" to stop Central American gangsters coming to the United States.

Bitter disputes continue about the border wall and who will pay for it; about the how to remake the North American Free Trade Agreement; and about possible deportations of Mexicans from the United States.

And yet the United States and Mexico also last month drank champagne toasts to their relationship and the start of construction on a giant, new, nearly $1 billion embassy building, with the outgoing U.S. ambassador, Roberta Jacobson, raising her glass "to the next 100 years or more."

"Our bilateral relationship has grown, diversified and accelerated, making it high time for us to trade in for a larger, modern and gorgeous new model," Jacobson told the crowd at the groundbreaking.

Despite the Trump-era tensions, the diplomatic work between the two countries remains robust. The U.S. Embassy houses some 1,200 to 1,400 diplomats, among the largest American missions in the world, according to U.S. officials. In addition, more than 1,000 other diplomats are posted around Mexico at nine consulates.

To some degree, the strain created by Trump's criticism of Mexico is counter-balanced by these extensive diplomatic and citizen ties. The two countries are among one other's top trading partners. Millions of Americans visit Mexico each year as tourists, and thousands of U.S. companies operate there.

The current embassy has been located since the mid-1960s along Reforma avenue, one of the city's main arteries and a favorite site for protests and marches. While centrally located, it has grown crowded over the years. Not only does it accommodate staff from many different agencies, including large contingents from the departments of Justice, Defense and Homeland Security, it grew steadily during the Obama administration. Reports from the State Department inspector general in 2009 and 2015 showed that total U.S. personnel in Mexico grew from 2,162 to 2,704 over that period.

"The embassy had simply become too small," said Carlos Pascual, the U.S. ambassador from 2009-2011 who began the search for a site for a new compound that would provide more room. Better security was also a factor. While it is centrally located, the current building has no setback and looming directly over the street -- in contravention of requirements for embassies built in the war-on-terror era.

Finding a big enough swath of land for a new building was not an easy task in this teeming capital; Jacobson called it "harder than crossing the city during rush hour in the rain."

Many embassies have been moving to peripheral parts of town, but Pascual wanted to find something central "in order for people in the embassy to have access to their counterparts in government and business."

The 8.5-acre site that was eventually found is about three miles northwest of the current embassy. The U.S. government arranged to purchase the land in 2011 from Colgate-Palmolive, which had a factory there for years.

The chemical pollutants left by the factory led to years of delays as Colgate-Palmolive cleaned up the site, and the expected cost of the project jumped by hundreds of millions of dollars.

"It's a bit of a fiasco," Rep. Jason Chaffetz (R-Ut) told CBS News in 2015. "I'm not going to step in there with the dirt with all [those] toxins in it."

Last week, Mexico's richest man, Carlos Slim, who owns swaths of the neighborhood, the city's mayor, Miguel Angel Mancera, Jacobson and several other officials and diplomats all happily tromped in that dirt for the groundbreaking ceremony.

Despite the lingering tensions, the Mexican officials struck a mostly positive note. Carlos Manuel Sada, the top official for North America at Mexico's Foreign Ministry, called the relationship "highly dynamic, which frequently presents us challenges, but also multiple agreements and opportunities." Interior Minister Alfonso Navarrete Prida described the United States and Mexico as "two nations with strong bonds and with enormous challenges" but added that, ultimately, "our house is also your house."

Still, Jacobson’s planned departure adds further uncertainty to the relationship. A longtime diplomat and Latin America expert, she is widely liked by Mexican officials, who have expressed worry that Trump might bring in a more combative envoy.

At the groundbreaking, a white tent was erected in the middle of the dirt expanse and servants in white gloves circulated with trays of champagne. The U.S. and Mexican officials hoisted gold-colored shovels wrapped in their respective flags to pitch the first piles of soil.

The project is expected to cost $943 million, according to the State Department.

The U.S. government completed the purchase from Colgate-Palmolive in 2016 and awarded the design contract to a joint venture between two New York-based architecture firms, Tod Williams Billie Tsien and Davis Brody Bond. An Alabama-based firm, Caddell Construction, was awarded the construction contract last year. Caddell has also built two of the eight prototypes for Trump's border wall in San Diego.

One of Caddell's representatives, Rod Ceasar, vice president for international operations, surveyed the dusty vacant lot last week with satisfaction.

"It's nice," he said. "It's flat. It's not wet."

"We're getting ready to start a big hole in the ground," he said. "We're excited about that."

On the streets around the site, not everyone is so thrilled. Humberto Nuñez, a mechanic, has watched with some concern the changes in his neighborhood, including the gradual departure of factories that made shampoo, screws and windows.

He's heard how eager developers are referring to the area, Colonia Irrigacion, by a new name -- Nuevo Polanco, after the famously swanky enclave to the south. The gentrifying creep has brought rising rents and more traffic.

"This neighborhood has changed radically in the last three or four years," said Nuñez, 50. "With the embassy, it will change even more."

Some neighbors say they afraid they might be priced out when U.S. diplomats descend. The sour view that many Mexicans have of  Trump has not helped the mood. In Trump's first year, Mexico has ridden a currency roller coaster, with the peso fluctuating according to news of the NAFTA negotiations and other factors.

"Whatever he says changes the value of the peso and generates uncertainty," Nuñez said. "You can't denigrate and insult people like this."

The embassy is expected to be completed in 2022.

"I hope they don't finish it until 2030. Maybe I'll be retired," said Valentin Lopez, 58, a carpenter who was building a desk inside his shop on Presa Las Virgenes street, along the southern edge of the construction site. "It's a bad idea for me. It might drive me away."

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