Secretary of State Antony J. Blinken and other top American officials were meeting with Mexico’s president on Wednesday for talks on how to slow the surge in illegal migration at the southern U.S. border.

President Biden dispatched the officials to Mexico City in a time when border crossings have hit record numbers. There have been days this month when the U.S. Border Patrol encountered more than 10,000 people making crossings.

Immigration has been a consistent political vulnerability for Mr. Biden, particularly as Republicans in Congress demand a new crackdown in exchange for wartime aid for Ukraine and Israel.

Mexico is a key player in the U.S. government’s efforts to limit the numbers of migrants, especially in recent years as people from across the globe have passed through the country in skyrocketing numbers.

Shortly before Wednesday’s meeting, President Andrés Manuel López Obrador of Mexico said the U.S. Congress should offer more support to Latin America instead of putting up “barriers, barbed wire fences on the river or thinking about building walls.”

“It is more efficient and more humane to invest in the development of the people,” he said.

He also said next year’s presidential election in the United States would bring migration to the top of the agenda.

“The migration issue is going to intensify,” he said.

During the Trump administration, Mexico agreed to take migrants under the former president’s “Remain in Mexico” policy. The migrants waited in border towns for months as they awaited court hearings in the United States, a key pillar of Mr. Trump’s crackdown on asylum seekers.

Later, during the institution of Title 42, a measure that allowed border agents to quickly expel asylum seekers, Mexico agreed to take in migrants from other countries.

Mr. Biden has struggled to keep the numbers down despite trying to institute limits on asylum access at the border and deporting migrants to Venezuela and Cuba.

He has also said he is willing to make “significant compromises” with Republicans on the border, if Republicans will agree to aid for Ukraine and Israel.

Wednesday’s meeting also included Alejandro N. Mayorkas, the homeland security secretary, and Liz Sherwood-Randall, the White House homeland security adviser.

A caravan that began its journey north on Sunday reflects the enormous challenges in stemming the tide of migration. Migrant caravans have become a common phenomenon and are usually broken up by the authorities well before they reach the U.S. border.

The latest caravan, roughly 1,000 miles south of the U.S. border in the state of Chiapas, includes people from Honduras, Haiti and Cuba, among other countries. The Mexico office of the U.N. refugee agency said in a statement that the procession was starting to disperse and consisted of around 3,000 people.

It initially included approximately 5,000 people, the agency said.

Republicans have stepped up their attacks on Mr. Biden over the border numbers, a continuing issue for the president as he seeks re-election next year. In Texas, Gov. Greg Abbott signed a law that authorizes law enforcement officials in his state to arrest migrants who cross without authorization. (El Paso County challenged the measure in federal court last week.) The president has also faced pressure from mayors in Democratic cities over the increase in migrants arriving in their cities.

The increase in border crossings in recent weeks has forced border officials to shut down railway crossings temporarily in El Paso and Eagle Pass, Texas, and to close the port of entry in Lukeville, Ariz. While the railway crossings are reopened, Biden administration officials plan to speak to Mexican officials about the port of entry closures, officials said in a statement.

Last week, Mr. López Obrador briefed reporters about a call with Mr. Biden in which they agreed that more enforcement at the border was needed.

“Now we have an extraordinary situation because the number of migrants passing through our country with the purpose of reaching the United States has increased,” he said, adding that Mexico was “going to help, as we always do.”

U.S. Customs and Border Protection officials announced on Friday that there were more than 190,000 apprehensions between ports of entry in November. U.S. officials said they “removed or returned” more than 400,000 people between May and the end of November.

“We are facing a serious challenge along the southwest border, and C.B.P. and our federal partners need more resources from Congress — as outlined in the supplemental budget request — to enhance border security and America’s national security,” Troy Miller, the acting leader of the border agency, said in a statement on Friday.