TEHRAN (Tasnim) - Thousands of migrants in southern Mexico have accepted a government offer to quit a US-bound caravan in exchange for Mexican visas.

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That's according to officials - who on Tuesday night said the migrants accepted a proposal to (quote) "begin the process that will allow them to regularize their legal status" in Mexico.

Haitian migrant Dunel Sineas said he was glad to soon be able to work. "We are happy and content. Thank God they will give us papers (a Mexican visa) to go to another city and support our family. Thank you very much."

The caravan is one of two large groups of migrants, many from Central America and the Caribbean, that left the southern city of Tapachula in recent weeks en route to the US border.

The caravan organizer told Reuters most of the migrants accepted the government offer and that officials would eventually bus them out of Chiapas and into other Mexican states.

But some migrants said waiting for change has been rough.

"We have been here for five days lying on the floor, women, men, children, sick people, with the supposed promise that they were going to give us a document to be able to transit (through the country) and finish the procedures we have started here in other states," said a Cuban migrant named Iliana. "Everything has been a lie. The immigration officials give us no answer, and the government says nothing."

A Mexican migration official told Reuters that an earlier group of migrants from Haiti and Honduras were taken to another state, some 620 miles away on Tuesday.

Washington has urged Mexico to keep migrants in check as the number of people stopped while attempting to cross the US border has more than doubled this year.