Protesters march in Mexico City in an August demonstration against NAFTA. Polls show most Mexicans support the free-trade pact, but farmers, union members and others are critical of its effects. (Anadolu Agency/Getty Images)

Secretary of State Rex Tillerson kicks off a Latin American swing on Thursday at a time of precarious relations with the United States' southern neighbor, with Mexicans offended by the Trump administration's positions on immigration and trade and the country's diplomats on an all-out offensive to preserve NAFTA.

The first year of the Trump administration has brought little clarity to the most contentious issues in the bilateral relationship. Several of Trump's key campaign promises still hang over Mexico like a dangling sword — to revise or potentially cancel NAFTA, to build a new border wall, to deport large numbers of unauthorized immigrants.

The relationship is crucial to both sides. Mexico is the No. 3 trading partner of the United States, while the United States is Mexico's largest partner, the destination for about 80 percent of its exports. The two countries have a vast web of ties on issues such as security to immigration. But uncertainties loom, from Trump's policies and the possibility that a less-accommodating Mexican leader might emerge from the July presidential election here.

"What has been a good relationship between the two countries right now is fragile and delicate," said Francisco Gil Villegas, a professor of international relations at the College of Mexico. "On the government level, they have avoided a crisis. On the citizen level, there is a lot of anger."

Tillerson's week-long trip, which starts in Mexico and includes stops in Argentina, Colombia, Peru and Jamaica, will focus on the crisis in Venezuela, the State Department said. But the United States is also balancing a full slate of delicate issues with Mexico, particularly the renegotiation of NAFTA, the North American Free Trade Agreement. Tillerson will encounter a region that has grown increasingly frustrated with Trump's protectionist rhetoric and his drive to reduce immigration.

Current and former officials have feared that such tensions could spill over into the crucial security relationship. Mexico and the United States share information on travelers between their countries as part of their anti-terrorism cooperation and collaborate on fighting drug traffickers.

So far, those partnerships have not fundamentally changed, current and former officials said. Mexico's national security commissioner, Renato Sales, said Tuesday that his country is in talks with U.S. officials about allowing American air marshals with stun guns to travel on cross-border flights by U.S. airlines, a joint effort first reported by Reuters.

"The relationship between the governments has been characterized by much tension and complexity, with the Mexican government making a great effort not to damage the status quo," said Gabriel Guerra Castellanos, a political analyst who runs a consulting firm here. "The diplomacy of this government has avoided a major crisis in relations with the United States."

Foreign Minister Luis Videgaray has been at the center of that effort, in part because of the close ties he developed during the U.S. presidential campaign with Trump's son-in-law, Jared Kushner.

Videgaray, as well as Economy Secretary Ildefonso Guajardo, have spearheaded Mexico's push to save NAFTA. Videgaray's relationships with top U.S. officials, including White House Chief of Staff John F. Kelly, have helped open doors across government agencies for Mexican officials.

Videgaray made 12 trips to Washington last year — often traveling on a Mexican navy airplane and landing at a private hangar at Dulles International Airport.

"He had, and he still has, one of the golden keys to the White House. Not a lot of people and not a lot of countries have that key," said a Mexican official who spoke on the condition of anonymity because he was not authorized to comment publicly. That access to Trump administration officials "allows us to try to make a couple of phone calls or to be able to defuse or neutralize or change minds, to put some pressure here or there," the official said.

In all, Mexican cabinet secretaries made 33 visits to the United States last year, whereas U.S. cabinet members visited Mexico 12 times, according to Mexico's Foreign Ministry. Mexico has also sought to enlist the help of U.S. governors, congressional representatives and business leaders who want to preserve NAFTA.

Mexican authorities say this access has given them crucial maneuvering room. On the day in April that Mexicans call "Black Wednesday," when Trump discussed issuing an executive order withdrawing from NAFTA, Mexican President Enrique Peña Nieto and Canadian Prime Minister Justin Trudeau successfully lobbied Trump over the phone not to take the step.

But others say the Mexican government's access to the White House has not yet won it anything concrete.

"Contact alone is not sufficient," said Michael Camuñez, an assistant secretary of commerce in the Obama administration who now runs a firm that advises U.S. companies on doing business in Mexico. The country's officials are "there for purely defensive reasons," he said. "They're in damage-control mode."

Trump's rhetoric about Mexico — including a recent tweet that falsely called it "the number one most dangerous country in the world" — is eroding Mexican authorities' trust in and respect for their U.S. counterparts, said Rebecca Bill Chavez, a deputy assistant defense secretary for Western Hemisphere affairs in the Obama administration.

The anger is "boiling under the surface," she said.

The Mexican presidential election in July could swing the relationship with the United States in a starkly new direction. The front-runner is leftist Andrés Manuel López Obrador, a former Mexico City mayor. The ruling party's candidate, José Antonio Meade, has been in third place in recent polls.

Some analysts say López Obrador could adopt a more confrontational policy toward Washington. The populist leader has criticized the Trump administration's moves to deport unauthorized immigrants and promised to end a relationship of "subordination" to the United States. López Obrador has been critical of NAFTA in the past, although he is presenting himself as a more moderate, pro-business candidate this time around.

"Without being disrespectful, we're going to put him in his place," López Obrador said of Trump in January.

Gabriela Martinez contributed to this report.