Several thousand members of a migrant caravan from Central America have rejected an offer from Mexico to stay and apply for asylum in that country, seeking to instead continue north toward the U.S.

The Associated Press reports that more than 1,700 members of the caravan have accepted offers from Mexican authorities, including the country's president Enrique Peña Nieto, to stay in Mexico and apply for asylum there.

Thousands of others continued north, according to the news service, after vowing to continue on their long trek to the U.S.

“Our goal is not to remain in Mexico,” one migrant from Honduras told the AP. “Our goal is to make it to the [U.S.]. We want passage, that’s all.”

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President Trump Donald John TrumpBiden says voters should choose who nominates Supreme Court justice Trump, Biden will not shake hands at first debate due to COVID-19 Pelosi: Trump Supreme Court pick 'threatens' Affordable Care Act MORE has pressured Mexico and Honduras to stop the caravan before it reaches the U.S. border, and he has used the caravan comprised mostly of families seeking asylum in an effort to rile up GOP voters ahead of the November elections.

“I am watching the Democrat Party led (because they want Open Borders and existing weak laws) assault on our country by Guatemala, Honduras and El Salvador, whose leaders are doing little to stop this large flow of people, INCLUDING MANY CRIMINALS, from entering Mexico to U.S.,” the president tweeted earlier this month.

The Trump administration has weighed a number of efforts to halt or turn back the caravan. On Friday The Washington Post reported that Trump was reportedly considering a plan that would bar all residents of Central America from applying for asylum, a move that would represent a major shift in U.S. asylum policy and cut off thousands of migrants who say that gangs and criminal activity make their home countries unsafe.

"We shall work with our partners in the region to investigate and prosecute to the fullest extent of the law all who seek to encourage and profit from irregular migration," Homeland Security Secretary Kirstjen Nielsen Kirstjen Michele NielsenMore than million in DHS contracts awarded to firm of acting secretary's wife: report DHS IG won't investigate after watchdog said Wolf, Cuccinelli appointments violated law Appeals court sides with Trump over drawdown of immigrant protections MORE said last Sunday.

"We fully support the efforts of Guatemala, Honduras and Mexico, as they seek to address this critical situation and ensure a safer and more secure region.” ­