Migrants were streaming across the U.S. southern border in record numbers, international rail bridges were abruptly shut down and official ports of entry closed.

Desperate for help in December, President Biden called President Andrés Manuel López Obrador of Mexico, who told him to quickly send a delegation to the Mexican capital, according to several U.S. officials.

The White House rushed to do so. Soon after, Mexico beefed up enforcement. Illegal border crossings into the United States plummeted by January.

As immigration moves to the forefront of the U.S. presidential campaign, Mexico has emerged as a key player on an issue with the potential to sway the election, and the White House has worked hard to preserve Mr. López Obrador’s cooperation.

The administration says publicly that its diplomacy has been a success.

But behind closed doors, some senior Biden officials have come to see Mr. López Obrador as an unpredictable partner, who they say isn’t doing enough to consistently control his own southern border or police routes being used by smugglers to bring millions of migrants to the United States, according to several U.S. and Mexican officials. None of them would speak on the record about delicate diplomatic relations.

“We aren’t getting the cooperation we should be getting,” said John Feeley, former deputy chief of mission in Mexico from 2009 to 2012. Mr. Feeley said the two countries did more joint patrols and investigations to secure the border during the Obama administration.

“I know what it looks like when there is genuine cooperation,” Mr. Feeley said, “as opposed to what we have now, which is being touted as great cooperation but I think is bupkis.”

While in office, President Donald J. Trump used the threat of tariffs to coerce Mr. López Obrador into implementing his crackdown on migration.

Mr. Biden needs Mexico just as much, but has taken a different approach, focusing instead on avoiding conflict with the powerful and sometimes volatile Mexican leader in hopes it will preserve his cooperation.

“AMLO has correctly assessed his leverage and has acknowledged that we’re using ours,” said Juan Gonzalez, Mr. Biden’s former top Latin America adviser, using Mr. López Obrador’s nickname.

Liz Sherwood-Randall, U.S. homeland security adviser, said that the White House works “collaboratively at the highest levels with the government of Mexico,” adding: “President Lopez Obrador has been a critically important partner to President Biden.”

Since 2022, Mexico has added hundreds of immigration checkpoints and increased enforcement personnel tenfold, according to figures provided by the U.S. State Department. Mexico is also detaining more migrants than at any point in recent history.

Yet, the numbers arriving at the southern border have remained stubbornly high. There were more than two million illegal border crossings in each of the last two fiscal years, twice as many as in 2019, the busiest year for apprehensions under Mr. Trump.

The lull at the start of this year was still one of the highest January months on record for illegal crossings, according to U.S. federal data. Apprehensions ticked up again in February.

In Mexico, officials say they have reached the limit of what they are able to achieve in the face of an extraordinary influx that has overwhelmed their country, too.

Mr. López Obrador has pushed the White House to commit more development aid to Latin American countries, to address the issues that cause migrants to leave in the first place.

“We do want for the root causes to be attended to, for them to be seriously looked at,” he told CBS’s “60 Minutes” in an interview that aired on Sunday. When asked whether he would continue to secure the border even if the United States didn’t do what he asked, Mr. López Obrador said, “Yes, because our relationship is very important.”

Migration has spiked because of factors difficult for any one government to control: persistent poverty, raging violence, the effects of climate change and the lingering impact of the coronavirus pandemic that have left people desperate for any chance at survival.

Yet Mexican officials also blame American policies, saying migrants have an incentive to come to the United States because the asylum system is so backlogged that migrants have a good chance of staying in the country for years until their case has been decided.

“This is entirely the responsibility of the United States, not ours,” Enrique Lucero, the head of the Migrant Affairs Office in Tijuana, a local government agency, said in an interview, referring to the migrant crisis.

The American government “needs to change their entire immigration and asylum system, the legal framework,” he said, “otherwise we end up doing the dirty work.”

In recent months, the authorities in Tijuana have raided hotels and safe houses, increased security at official crossings and installed new checkpoints along a once-deserted section of the border near the city where migrants were passing through a gap in the wall.

Nothing worked for long.

The authorities’ crackdown has only put migrants in greater danger, aid groups say, leading smugglers to take people on riskier routes through the vast desert, where they often get lost and are found dehydrated.

One night in February, a smuggler dropped a group of 18 people miles from the border, telling them they would quickly find a gap in the wall. In the darkness, the group got lost and walked for hours until finally crossing into California and making it to a makeshift camp where migrants often squeeze into portable bathrooms for shelter.

Two-year-old Denver Gonzalez could not stop sobbing.

“I am cold, I want to sleep,” the boy screamed repeatedly, as his father wrapped his tiny frame in blankets donated by a local volunteer.

“You pressure them at one point, and they go to another place,” said David Pérez Tejada, head of the Baja California office of Mexico’s National Immigration Institute, referring to the smugglers. “It’s all a game of cat and mouse, and it is extremely difficult to control this.”

The White House has pushed the Mexican government to increase deportations, implement visa restrictions for more countries to make it difficult to enter Mexico and bolster security forces at its southern border.

Since 2022, the Mexican government has added hundreds of immigration checkpoints, bolstered security along train routes used by migrants to travel north and increased enforcement personnel tenfold, according to figures provided by the U.S. State Department. Mexico is also detaining more migrants than at any point in recent history.

Yet truckloads of migrants continue to drive up through the country, in part because smugglers often pay off the checkpoint authorities, U.S. officials say.

The Biden administration wants Mexico to increase deportations. Mexico’s foreign ministry said last week it had reached an agreement with Venezuela to deport migrants and help them find jobs.

But repatriation flights are expensive, and Mexico has legal barriers to deporting people en masse. Last year, the Mexican Supreme Court ruled that migrants could only be detained for 36 hours.

Many countries ask for at least 72 hours notice before accepting flights with their citizens, said a senior Mexican official who was not authorized to speak publicly. That means the government often has to release migrants before it can negotiate their return. Deportations from Mexico dropped by more than half last year, Mexican government data show.

The White House has also pressed Mexico to do more of what some officials call “decompression,” which involves transporting people away from the border to somewhere deep in the country.

“People are being detained by Mexican authorities and sent to random cities in the south,” said Erika Pinheiro, executive director of Al Otro Lado, or “To the Other Side,” a humanitarian group. “Forcing them to trek back north, pay bribes to authorities and take all those risks all over again is inhumane.”

Emiliano Rodríguez Mega contributed reporting from Mexico City.