After meeting with President Donald Trump on Tuesday, Senate Majority Leader Mitch McConnell, (R-Kentucky), said that he and the rest of the Republican caucus plan to work on legislation that would end the practice of separating migrant families at the country's southern border.

“I support, and all of the members of the Republican conference support, a plan to keep families together while their immigration status is determined,” McConnell said.

>>President Trump to reverse course on immigrant family separations

McConnell is the highest-ranking Republican to publicly disagree with Trump on the “zero tolerance” immigration policy announced in April by U.S. Attorney General Jeff Sessions. The policy calls for adults illegally entering the country to be criminally prosecuted.

Children who accompany those arrested for illegally entering the country are separated from their parents or guardians and taken into the custody of the Department of Health and Human Services.

Photographs of children behind fenced areas inside large facilities and an audio tape of children crying for their parents have led legislators to call for Trump to immediately end the policy of separating migrant families.

According to immigration records, during April and May, federal authorities separated at least 1,995 children from parents apprehended crossing the border illegally.

>>Clergy group brings church charges of child abuse, immorality against Jeff Sessions over zero-tolerance policy

Sen. Ted Curz, (R-Texas), introduced a bill Tuesday that would require children be kept with their family members unless the child appeared to be in danger or the victim of human trafficking. The bill calls for doubling the number of federal immigration judges and authorize new family shelters.

Also on Tuesday, Sen. Orrin Hatch, (R-Utah), and a dozen other Republican senators sent a letter to Sessions asking him to stop the policy of separating migrant families while Congress works on a solution to the issue.

The letter read in part: "The immediate cause of the crisis is your Department's recent institution of a 'zero tolerance' policy under which all adults who enter the United States illegally are referred for prosecution, regardless of whether they are accompanied by minor children. We support the administration's efforts to enforce our immigration laws, but we cannot support implementation of a policy that results in the categorical forced separation of minor children from their parents.”

Those senators signing the letter:

Sen. Lamar Alexander (Tennessee)

Sen. John Boozman (Arkansas)

Sen. Bill Cassidy (Louisiana)

Sen. Susan Collins (Maine)

Sen. Bob Corker (Tennessee)

Sen. Cory Gardner (Colorado)

Sen. Dean Heller (Nevada)

Sen. James Lankford (Oklahoma)

Sen. John McCain (Arizona)

Sen. Lisa Murkowski (Alaska)

Sen. Rob Portman (Ohio)

Sen. Pat Roberts (Kansas)

Here are some other Republicans who have spoken out against the policy:

Florida Sen. Marco Rubio

Missouri Sen. Roy Blunt

“We clearly have a border security problem," Blunt said in a statement to KCUR. "I agree with Mrs. [Laura] Bush and Mrs. [Melania] Trump that separating families does not meet the standard of who we are as a country. Strengthening our border security and upholding our laws in a manner consistent with our values will help facilitate progress toward addressing all aspects of our broken immigration system.”

Kansas Rep. Kevin Yoder

“As the son of a social worker, I know the human trauma that comes with children being separated from their parents,” he tweeted. “It takes a lasting, and sometimes even irreversible toll on the child’s well-being. That’s why I’m demanding that Attorney General Sessions halt the practice of family separation at the border immediately as Congress works toward legislative solutions.”

Texas Sen. John Cornyn

“Parents who are awaiting court proceedings shouldn’t have to do so separated from their children, and children shouldn’t be taken from their parents and left frightened and confused about where they are and what is transpiring around them.”

Colorado Rep. Mike Coffman

“This afternoon I reached out to Sen. Diane Feinstein’s office to let her know I want to help her put a stop to this human rights disaster at the border. If that means introducing her bill in the House, I’d be honored to stand with her. If there is a better bill sponsor to get this done, or if there is a better approach from Sen. Ben Sasse, I’m open to all reasonable options. Tearing children from the arms of parents and then isolating them alone is antithetical to the America I grew up in, and to the America I have fought many times to defend. This isn’t who we are. My colleagues should mark their words and this moment — history won’t remember well those who support the continuation of this policy.”

Nebraska Sen. Ben Sasse 

“The president should immediately end this family separation policy.”

Texas Rep. Will Hurd

“This is part of the problem with this administration on this policy. There's different elements of the government that don't understand what's really going on. Kids are being separated from their parents. In the last two months, there's been about 2,000. The previous year, it was almost 700. And a hundred of those kids were under the age of 4. This is just absolutely unacceptable. Taking kids from their mothers is not preventing terrorists or drugs from coming into this country.”

Ohio Rep. Steve Stivers 

“I will support other means to stop unnecessary separation of children from their parents.”

New Jersey Rep. Chris Smith

"There is nothing more important than protecting vulnerable children from physical and psychological harm. The policy of forcibly separating children from their parent or parents at the U.S. border is seriously wrong, hurts families, and needs to immediately end.

"The departments of Justice and Homeland Security must halt the practice of family separations, except in the cases of criminal felonies by an adult including rape, murder, sexual assault on a minor, or human trafficking."

Not calling out the Guard

Governors of at least 13 states have said they will not send their state's National Guardsmen to help secure the southern border, according to a story from The New York Times.

The governors of Connecticut, Delaware, Maryland, Massachusetts, New Hampshire, New Jersey, New York, North Carolina, Oregon, Pennsylvania, Rhode Island, Vermont and Virginia have all said they will not deploy National Guard troops to the southern border.

Governors of other states have said they will not use state resources to separate adults from children at the border.

In April, Trump called on the country's governors to deploy more National Guard troops to the border to help with border security. State governors control National Guard deployment.

Most of the governors who have said they will either recall or refuse to send troops are Democrats. Two of the governors who have spoken publicly about National Guard troop deployment to the border are Republicans – Maryland Gov. Larry Hogan and Massachusetts Gov. Charlie Baker.

The role of National Guard troops is limited. National Guard troops are forbidden by the Posse Comiatus Act from detaining suspects, from using force or from other law enforcement functions. Their role at the border would be one of providing support and possibly helping in surveillance.