Thousands of Central American migrants, mainly from Honduras, continued their arduous northbound journey through Mexico on Wednesday in their push to reach the United States.

Traveling mostly on foot, migrants such as the Honduran-born Franco, are driven by the promise of finding better work opportunities.

"The only thing I am thinking about is getting to the next town, step by step," Franco told Xinhua as he was about to trek through jungle between the community of Mapastepec, in southern Chiapas state, and the neighboring state of Oaxaca.

Like thousands of others, Franco set out from the northern Honduran city of San Pedro Sula on Oct. 13 as part of a caravan of undocumented migrants.

The caravan started out with 1,200 people but has swelled to some 7,000, as others joined from El Salvador and Guatemala.

The migrants, including men, women and children, are pressing on despite U.S. President Donald Trump's threat to close the border to prevent their entry.

Their desperate attempt to improve their lives and those of their children has put enormous pressure on Mexican President Enrique Pena Nieto, as Trump demands Mexican authorities take steps to stop the caravan's progress.

Mexico's government is recommending the migrants legalize their stay in the country by processing the required paperwork, and lawmakers have called on authorities to guarantee the migrants' human rights and attend to their needs.

The Senate has asked the government to "promptly respond to those requesting refuge."

On Tuesday, Mexican Foreign Affairs Minister Luis Videgaray spoke by telephone with U.S. Secretary of State Mike Pompeo about his country's efforts to attend to the migrants with the help of the United Nations High Commissioner for Refugees (UNHCR).

So far, Mexico's immigration institute has received 1,699 applications for refugee status from migrants who entered legally as part of the caravan that crossed into the country on Oct. 19.

Xinhua reporters have been following the sometimes hazardous progress of the caravan, which is now heading to Oaxaca. On Monday, a 25-year-old migrant was killed when he fell from a railcar.

Once they have reached a town, the migrants usually come to rest at a square, where local officials have set up temporary shelters in cooperation with local religious or civic organizations.

On Wednesday, Trump again threatened to bar their entry, saying via Twitter "We have strong borders and will never accept people coming into our country illegally!"

Earlier Trump said he might send army troops to the border to prevent the migrants' entry. He also proposed penalizing Honduras, El Salvador and Guatemala, for their failure to stop the migrants, by suspending U.S. aid to those countries.

The caravan isn't expected to arrive at the U.S.-Mexico border until December, and Mexico's president-elect Andres Manuel Lopez Obrador, who takes office on Dec. 1, has offered to grant the migrants temporary work visas.

To curb northward migration, which is a major concern for Trump, Lopez Obrador plans to generate jobs through large-scale infrastructure projects, especially in Mexico's poorer southern states. He has invited the United States and Canada to take part in the scheme.