MEXICO CITY - A controversial bid by US President Donald Trump to deport non-Mexican illegal migrants to Mexico will top the agenda when officials from both countries were scheduled to meet on Thursday amid a deepening rift between the two nations.

The US government on Tuesday said it would seek to deport many illegal immigrants to Mexico if they entered the United States from there, regardless of their nationality, prompting a fiery response from Mexican officials.

Calling the measure "unilateral" and "unprecedented", Mexican Foreign Minister Luis Videgaray said new immigration guidelines would top the agenda of meetings with US Secretary of State Rex Tillerson and Homeland Security Secretary John Kelly.

The stakes are high for the US, since Mexico has warned that a breakdown in relations could affect its extensive cooperation on the fight against narcotics and on stemming the flow of Central American migrants that reach the US border.

Talking points from a senior official show Mexicans plan to seek more information on Trump's executive orders at the meeting. Officials plan to say: "We are worried about the consequences that these can have for Mexican nationals" in the US, the notes showed.

As part of its response, Videgaray said the Foreign Ministry would get involved in legal cases in the US where it considered the rights of Mexicans had been violated.

The visit, which would also include meetings with Mexican President Enrique Pena Nieto, was supposed to focus on border security, law enforcement and trade, according to the state department.

Tensions deepened

But hopes for a thawing in relations are low, after a series of botched meetings last month deepened tensions between the historic allies.

"The relationship ... is at such a historic low that it would be wishful thinking to assume that new concrete agenda items to advance will come at this point," said Jason Marczak, director of the Atlantic Council's Latin America Economic Growth Initiative.

Pena Nieto abruptly canceled a planned January summit with Trump after the real estate mogul suggested the Mexican leader should not come if he refused to pay for a border wall.

And Trump signed his first executive orders to punish sanctuary cities and build the wall, which could cost around $21.6 billion.

Trump has also threatened to rip up a trade deal between the US and Mexico if he cannot renegotiate it to favor US interests.

US Secretary of State Rex Tillerson arrives in Mexico City on Wednesday.Carlos Jasso / Reuters