MEXICO CITY (AP) — The remnants of a caravan of Central American migrants protested in northern Mexico on Monday, even as once again they drew angry tweets from U.S. President Donald Trump.

The mainly Central American migrants are demanding better treatment and many are planning to request asylum, either in the United States or Mexico.

"We are asking the government and migration authorities to respect the right to seek asylum," said caravan organizer Irineo Mujica. "Those who request asylum shouldn't be criminalized. It is a right ... families shouldn't be separated or punished."

The approximately 600 migrants arrived in the northern city of Hermosillo aboard trains over the weekend.

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Mujica has said the migrants plan to arrive in Tijuana later this week.

Trump tweeted Monday that "I have instructed the Secretary of Homeland Security not to let these large Caravans of people into our Country."

"Mexico, whose laws on immigration are very tough, must stop people from going through Mexico and into the U.S. We may make this a condition of the new NAFTA Agreement," Trump tweeted.

In response, Mexico's Secretary of Foreign Affairs Luis Videgaray tweeted, "It would be unacceptable to condition the NAFTA negotiations on immigration actions that are outside that framework."

"Mexico decides its own immigration policy in a sovereign manner, and Mexico's cooperation on immigration matters with the United States occurs because Mexico considers it in its own interest," Videgaray wrote.

Many of the migrants say they are fleeing gang violence and extortion in Honduras and El Salvador.

The U.S. government "should be more understanding of the women and children in this caravan ... and the dangers they face in their countries," Mujica said.

U.S. Attorney General Jeff Sessions said Monday that he told his offices in border states to "take whatever immediate action to ensure that we have sufficient prosecutors available" and that he may transfer immigration judges to the border. He said caravan members have ignored the Mexican government's willingness to let them stay in Mexico.

"Let today's message be clear: Our nation has the most generous immigration system in the world, but this is a deliberate attempt to undermine our laws and overwhelm our system," Sessions said.

U.S. Homeland Security Secretary Kirstjen Nielsen said Monday that "DHS continues to monitor the remnants of the 'caravan' of individuals headed to our Southern border with the apparent intention of entering the United States illegally."

"If members of the 'caravan' enter the country illegally, they will be referred for prosecution for illegal entry in accordance with existing law," Nielsen said in a statement. "For those seeking asylum, all individuals may be detained while their claims are adjudicated efficiently and expeditiously, and those found not to have a claim will be promptly removed from the United States."

She said her agency was working with the Justice Department in "taking a number of steps to ensure that all cases and claims are adjudicated promptly - including sending additional USCIS asylum officers, ICE attorneys, DOJ Immigration Judges, and DOJ prosecutors to the Southern border."

"DHS encourages persons with asylum or other similar claims to seek protections in the first safe country they enter, including Mexico," the statement said.