(CNN) — The Biden administration is preparing to roll out a sweeping border executive action as early as Tuesday, according to two sources familiar with the discussions, who cautioned that timing is fluid.

White House officials have begun reaching out to mayors who represent cities along the US southern border to potentially join President Joe Biden when he announces the order, two other sources familiar with those conversations said.

For weeks, administration officials have been working through an executive action that would dramatically limit migrants’ ability to seek asylum at the US southern border — part of a strategy to try to give Biden the upper hand on one of his Republican rival’s key campaign issues. The action is designed to potentially blunt Republican attacks on border security and preempt former President Donald Trump ahead of the first presidential debate, which will be held on June 27 on CNN.

Edinburg Mayor Ramiro Garza confirmed to CNN that the administration contacted him on Saturday to attend a Tuesday event at the White House.

The order is expected to be reminiscent of a controversial measure from the Trump era. It involves using an authority known as 212f between ports of entry to try to clamp down on unlawful border crossings.

CNN previously reported that officials were discussing announcing the executive action after Mexico’s election on Sunday and before the first presidential debate. Biden is scheduled to travel to France on Wednesday.

“While Congressional Republicans chose to stand in the way of additional border enforcement, President Biden will not stop fighting to deliver the resources that border and immigration personnel need to secure our border,” a White House spokesperson said in a statement. “As we have said before, the Administration continues to explore a series of policy options and we remain committed to taking action to address our broken immigration system.”

Several Texas mayors have previously expressed frustration over the hyperpolarization over immigration as tensions between Biden and Texas Gov. Greg Abbott escalated. During his February trip to the US southern border, Biden met with Garza, Brownsville Mayor John Cowen, San Antonio Mayor Ron Nirenberg, and Weslaco Mayor Adrian Gonzalez.

A White House official told CNN that no final decisions have been made on additional executive actions.

With border arrests down this year, thanks in part to Mexico stepping up its own enforcement efforts in January, the White House is looking to take advantage of a brief reprieve from one of the most politically fraught issues Biden faces in his reelection campaign.

Some Democrats on Capitol Hill have also encouraged White House officials to consider having the president make another visit to the border in the coming weeks. A White House spokesperson previously told CNN that no border trip for Biden is under consideration at the moment.

Over recent weeks, the administration has trotted out a series of policy changes to try to dissuade migrants from journeying to the US and convince skeptical voters they are working to tighten up immigration at the border.

That includes rolling out new guidance and regulations that would tighten the immigration system to quickly reject migrants who are ineligible for asylum and speed up court cases for some migrants — measures Biden officials hope will, in part, keep the number of border crossings low.

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