MEXICO CITY (Reuters) - Mexico wants to sharpen existing measures in its bid to narrow a flood of Central American migrants to the U.S. border, a top Mexican official said on Friday, ahead of planned meetings in Washington over tariffs threatened by President Donald Trump.

FILE PHOTO: Mexico's Deputy Foreign Minister for North America, Jesus Seade reacts during the delivery of the United States-Mexico-Canada Agreement (USMCA) deal at the Senate building in Mexico City, Mexico May 30, 2019. Picture taken May 30, 2019. REUTERS/Henry Romero

Trump on Thursday said he would introduce the tariffs, starting at 5% on June 10 and quickly ratcheting higher if Mexico did not substantially halt illegal immigration, largely from Central America, across the U.S.-Mexican border.

“To avoid these flows that go from Central America to the United States in large numbers I think we can make progress with traditional mechanisms and better exercise existing rules,” said Jesus Seade, Mexico’s deputy foreign minister for North America.

Asked if Mexico might agree to be classified as a “safe third country” where asylum seekers would have to lodge claims instead of the United States, he replied, “That is not something we are working with.”

Seade declined to give further details of what more Mexico could do to stem immigration, citing the delicate nature of the talks in Washington.

Trump’s ultimatum is the biggest foreign policy test yet for Mexican President Andres Manuel Lopez Obrador and a tall order for security forces already struggling to reduce migrant flows and combat record levels of gang violence and homicide.

Trump’s pressure has spurred Mexico to step up the number of undocumented immigrants it detains and deports in recent months, but numbers reaching the U.S. border have also risen.

Foreign Minister Marcelo Ebrard traveled to Washington on Friday and is to be joined by Seade on Sunday. On Wednesday they will meet a U.S. delegation led by Secretary of State Mike Pompeo to resolve the dispute.

Seade said the Mexican team was setting up other meetings for Monday and Tuesday, and had spoken ahead of the trip with the United States Trade Representative.

“I had a good conversation with (USTR) Robert Lighthizer, but in reality the issue at hand has more to do with immigration,” he added.

Trump has pledged to end the wave of tens of thousands of asylum seekers, including many Central American families fleeing poverty and violence, who make the arduous journey north to seek refuge in the United States.

In the biggest migrant surge on the U.S-Mexican border in a decade, U.S. officials say 80,000 people are in custody, with an average of 4,500 mostly Central American migrants arriving each day, overwhelming the handling resources of border officials.

The number of migrants arrested on the southwest border last month was 98,977, a record.

As part of the U.S. effort to stem the flow, Kevin K. McAleenan, the acting secretary of the Department of Homeland Security (DHS) and Guatemala government agreed to boost law enforcement cooperation, the DHS said on Friday.

“Included in the agreement is a provision on law enforcement training to improve criminal investigations that disrupt human trafficking and drug smuggling networks,” the DHS said in a statement.

Such networks are often run by transnational criminal groups that profit from human suffering, it added.

A Mexican government source said McAleenan and Guatemala’s government agreed on the presence of DHS “advisers” in the Central American nation, but Mexico was not part of the pact.

Since taking office in December, Lopez Obrador has urged Trump to help him tackle migration by promoting economic development in El Salvador, Guatemala and Honduras.