In April, a similar group of impoverished travelers failed to sway Donald Trump's "zero tolerance" stance on migration, which lead to the separation of migrants from Latin America illegally crossing the United States border.
Some 1,300 people joined the so-called "March of the Migrant" - just days after the USA urged Honduras' president to halt mass migration.
More than 1,000 people, including families and women carrying babies, set off on Saturday from Honduras towards the United States in a mass migration march.
On Monday, Guatemalan authorities announced that they would prohibit the entry of the Honduran migrants if they do not comply with Guatemala's entry requirements.
The migrants said they were fleeing violence and poverty in Honduras.
It was not clear how Honduras would be able to exercise control over people who had already left the country.
Last week, Vice President Pence met with leaders from Honduras, El Salvador, Guatemala and Mexico.
Hernandez said last month that cuts in US support for Central America would hinder efforts to stem illegal immigration, and welcomed China's growing diplomatic presence in the region as an "opportunity". From there, participants will request refugee status, which would allow them to stay in the country, or they will apply for a visa to pass through into the U.S.
Honduras is one of a dwindling number of countries that still has formal diplomatic ties with Taiwan.
The march started with fewer than 200 members in the Honduran city of San Pedro Sula one of the world's most risky places.
Hundreds of Hondurans have headed toward the American border fleeing poverty and violence, Reuters reported on Sunday, days after Washington pushed Latin American presidents for tighter borders. Guatemalan police initially blocked migrants from reaching a customs booth, Reuters images showed. Then it's on to Mexico and possibly the United States, though if history holds, numerous migrants will break off and remain in Central America.
The U.S. president and his conservative allies have warned that migrants bring rampant crime and drugs, despite studies that have shown immigration has little effect on crime rates.