Secretary of State Rex Tillerson arrives in Mexico City, Mexico Feb. 22, 2017. Reuters

Mexico's Foreign Minister Luis Videgaray rejected President Donald Trump's deportation policy Wednesday that could send millions of immigrants, not just Mexicans, over the southern U.S. border. Under the new guidelines on immigration, which were disclosed by the Trump administration Tuesday, almost all people living illegally in the U.S can be deported to Mexico.

"Remember, everybody who is here illegally is subject to removal at any time. That is consistent with every country, not just ours. If you're in this country in an illegal manner, that obviously there's a provision that could ensure that you be removed," said White House Press Secretary Sean Spicer in a press briefing Tuesday.

But Videgaray said his country could not "accept unilateral decisions imposed by one government on another," reported BBC News. The U.S. has suggested it could deport undocumented immigrants back to Mexico even if they are not Mexican citizens.

The disagreement occurs at a time when Secretary of State Rex Tillerson and Homeland Security Secretary John Kelly were visiting Mexico Wednesday. They were expected to discuss security, immigration, trade and the border with Mexican President Enrique Pena Nieto and other officials starting Thursday.

Meanwhile, thousands of Mexicans rallied in the streets Wednesday morning holding anti-Trump placards to protest future U.S. deportations to Mexico. Though it remains unclear whether the U.S. has authority to force Mexico to accept foreigners, Videgaray said Wednesday: "We are not going to accept that because we don't have to and it is not in the interest of Mexico."

Spicer has denied that Mexico is unhappy with Washington. He said the U.S. and Mexico "have a very healthy and robust relationship," USA Today reported. "I think they would echo that same sentiment," Spicer said. "I think the relationship with Mexico is phenomenal right now. I believe there’s an unbelievable and robust dialogue between our two nations.”