Interior Secretary Ryan Zinke on Tuesday said America can't give away the Rio Grande to Mexico in the process of building President Trump's signature border wall, implying the structure could wind up standing partially on Mexican land.

"The border is complicated, as far as building a physical wall," he said during a speech to the Public Land Council in Washington, D.C., according to E&E News

"The Rio Grande, what side of the river are you going to put the wall? We're not going to put it on our side and cede the river to Mexico. And we're probably not going to put it in the middle of the river."

Zinke reportedly conceded that the administration could instead rely on electronic defenses or could skip building the wall in certain areas where terrain may make crossing improbable. 

Democrats piled on Zinke for the remarks, accusing him of calling for the wall to be built in Mexico. 

Senate Minority Leader Chuck SchumerCharles SchumerDems wait for GOP olive branch after ObamaCare debacle How Obama's White House weaponized media against Trump Interior secretary hints border wall could be on Mexican land MORE (D-N.Y.) asked Wednesday morning to enter the quote into the record, moving on without any comment. But his spokesman, Matt House, needled Zinke in a tweet.

"These guys… now the wall is going to be IN Mexico, according to Interior Secretary Zinke," he said.

Americans Oversight, a watchdog group that's pushed back against the wall, piled on, too. 

"First, President Trump proposed building a wall on our southern border and having Mexico pay for it. Now his administration is planning to build a wall in Mexico and have Americans pay for it," Austin Evers, the group's executive director, said in a statement. 

"Logistically, this latest proposal to build the wall in Mexico raises a host of legal, procurement, and long-term issues."

A 1970 treaty negotiated between the United States and Mexico established the middle of the Rio Grande as the border in some places. That treaty, as well as the natural shifts of the river, served as a stumbling block to previous attempts to build border fencing and could complicate the Trump administration's push for a wall. 

Trump made the construction of a border wall to stem the flow of illegal immigration a centerpiece of his presidential campaign. Once in the Oval Office, Trump almost immediately signed an executive order calling for the wall to be built and the Department of Homeland Security has requested proposals. 

However, the plan is likely to face a difficult path. Sen. Roy BluntRoy BluntWhite House signals it can live without border wall funds Interior secretary hints border wall could be on Mexican land Republicans seek to lower odds of a shutdown MORE (R-Mo.), who plays a major role on the Appropriations Committee, told reporters that congressional leadership is likely to agree on a government spending bill soon and would rather deal with that funding as a supplemental bill later. 

As CNN reported on Tuesday, the Department of Homeland Security's first request for funding the project is about $1 billion to cover 62 miles with either new or replacement fencing.