Mexico's Foreign Minister Marcelo Ebrard holds a news conference next to National Immigration Institute Commissioner Francisco Garduno following talks with members of the Trump administration in Washington on Sept. 10. (Sarah Silbiger/Reuters)

A day after touting a decline in unauthorized immigration, the White House sought to redouble pressure on Mexico to interdict migrants, illustrating the sensitive balance for the administration as President Trump seeks to demonstrate progress on a key campaign promise.

In an afternoon meeting at the White House, Vice President Pence and Secretary of State Mike Pompeo sought to gain support from Mexican Foreign Minister Marcelo Ebrard to take additional steps to stem the record surge of Central American families that led to overcrowded border facilities in the spring. But in a sign that negotiations remain fraught, Ebrard told reporters afterward that he reiterated Mexico’s opposition to the Trump administration demands for a “safe third country” agreement that would require Central Americans to apply for asylum in Mexico.

The talks came as Trump aides have expressed cautious optimism over the past three months in which the number of migrants taken into custody at the border declined 56 percent from a 12-year high of 144,000 in May to 64,000 in August, according to federal data. The president and his aides have praised Mexico’s efforts, while acknowledging that more needs to be done, with some U.S. officials warning of signs that the numbers could spike again as the weather cools in the fall.

Pompeo, speaking to reporters ahead of the meeting, called the trends at the border “substantial and real and material,” and he said the more aggressive enforcement since Trump threatened to enact new tariffs on Mexico in early June have “made Americans more safe.”

But Pompeo added that “we know there is still work to do, and we’re going to talk about how best we can jointly deliver that.”

Trump, who had praised Mexico’s efforts at a campaign rally in Fayetteville, N.C., on Monday night, struck a triumphant tone, tweeting after the White House meetings: “Incredible progress being made at the Southern Border!”

The president’s tweet included a chart that appeared to show a sharp decline in the number of new Central American migrants who are able to remain in the United States after being taken into custody. The chart included no attribution source and is not a typical part of Customs and Border Protection metrics. An administration official said later that the chart was given to the president by the Mexican delegation.

In a short readout of the meeting, Pence’s office said he commended Ebrard for Mexico’s cooperation in dispatching thousands of its National Guard troops to the border with the United States, as well as the nation’s southern border with Guatemala. Pence also emphasized the need for Mexico to expand a program called the Migrant Protection Protocols, established this year, in which some asylum seekers who reach the United States are forced to remain in border towns in Mexico as their cases are processed, which could take months.

Ebrard told reporters that Trump joined the meeting for about 10 minutes as it wrapped up, telling the Mexican delegation he had a “positive impression” of its efforts at curbing migration. Trump and his aides did not renew the threat of tariffs, he said.

“What Mexico is doing has achieved results,” Ebrard said. “While we’re still above historic [migration] levels, this trend is irreversible. It’s something that we think will be permanent.”

He added that the Mexican delegation asked the Trump administration to do more to curb the flow of weapons southbound into his country, as Mexico grapples with an increase in murders and violent crime.

Experts said the administration’s wariness over taking a full victory lap for the decline in border crossings is a recognition that while the extraordinary spike in apprehensions in the spring has subsided, the number of migrants attempting to reach the country was higher last month than any August since 2007.

Theresa C. Brown, an immigration analyst at the Bipartisan Policy Center, compared border crossing trends to the stock market, noting it is risky to try to deduce trends based on limited data, given that the overall picture is based on many factors. She said the Trump administration is wary about giving Mexico too much leverage in their negotiations if it prematurely paints the border crisis as resolved.

“They are at least being somewhat nuanced because if they claim victory it could give Mexico an excuse to say, ‘See, we don’t need to negotiate a safe third agreement,’ ” said Brown, who served as a career policy official on immigration at the Department of Homeland Security until 2011. “It’s too soon to assess whether this is a long-term change, a short-term change, a blip. A lot is still in limbo.”

Immigrant rights groups have denounced the Trump administration’s strategy to reduce the number of asylum seekers, calling the MPP program unsafe for thousands of migrants stranded in border towns where drug cartels and human traffickers have considerable influence. The administration’s attempts to use regulatory changes to deny migrants the right to seek asylum have been repeatedly blocked in federal courts.

After the rising flow of migrants resulted in a humanitarian crisis at the border, Trump lashed out at Mexico in early June and threatened to enact escalating tariffs on all Mexican exports to the United States. Mexican officials rushed to Washington to hammer out an agreement, promising to employ more National Guard troops and take other measures.

Administration officials attributed much of the decline in border crossings to the steps that were taken, noting that the numbers, which usually dip in warmer summer months, have dropped at a greater rate than they have in past years.

But the magnitude of the challenge is made clear by just how the numbers spiked this year. The number of migrants taken into custody last month exceeds any single month last fall when Trump repeatedly railed at campaign rallies about a “caravan” of migrants streaming into the United States.

Kevin McAleenan, the acting homeland security secretary, has said the agency’s target is a return to the “historic lows” tallied at the border in the early days of the Trump administration, when U.S. agents were making fewer than 20,000 arrests per month.

Adam Isacson, a security analyst at the Washington Office on Latin America, said that goal puts unrealistic expectations on ­Mexico.

“Mexico is not East Germany,” he said. “It’s always going to be a place that is pretty permeable, especially when you have large numbers of people who want to leave their home countries and sophisticated smuggling networks that aren’t going out of business any time soon.”