More than a dozen Republican senators are asking the Trump administration to halt the separation of immigrant families at the U.S.-Mexico border while Congress works out legislation.

GOP senators, led by Sen. Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (Utah), sent a letter to Attorney General Jeff Sessions Jefferson (Jeff) Beauregard SessionsGOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status MORE asking for a moratorium of the president's controversial "zero tolerance" policy, which is resulting in the separation of families detained at the border.

"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," the Republican senators wrote.

"We therefore ask you to halt implementation of the Department’s zero tolerance policy while Congress works out a solution that enables faster processing of individuals who enter our country illegally without requiring the forced, inhumane separation of children from their parents," the senators continued.

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In addition to Hatch, GOP Sens. John McCain John Sidney McCainThe Memo: Trump's strengths complicate election picture Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' Cindy McCain: Trump allegedly calling war dead 'losers' was 'pretty much' last straw before Biden endorsement MORE (Ariz.), Pat Roberts Charles (Pat) Patrick RobertsThe Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill GOP senators say coronavirus deal dead until after election MORE (Kan.), Susan Collins Susan Margaret CollinsClub for Growth to spend million in ads for Trump Supreme Court nominee Maryland's GOP governor says Republicans shouldn't rush SCOTUS vote before election The Hill's Morning Report - Sponsored by Facebook - GOP closes ranks to fill SCOTUS vacancy by November MORE (Maine), Lisa Murkowski Lisa Ann MurkowskiClub for Growth to spend million in ads for Trump Supreme Court nominee Pebble Mine CEO resigns over secretly recorded comments about government officials Maryland's GOP governor says Republicans shouldn't rush SCOTUS vote before election MORE (Alaska), Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (Tenn.), Lamar Alexander Andrew (Lamar) Lamar AlexanderGraham: GOP has votes to confirm Trump's Supreme Court nominee before the election The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE (Tenn.), John Boozman John Nichols BoozmanCOVID-19 relief talks look dead until September Senate GOP hedges on attending Trump's convention amid coronavirus uptick The Hill's Coronavirus Report: San Francisco Gay Men's Chorus Artistic Director Tim Seelig says choirs are dangerous; Pence says, 'We have saved lives' MORE (Ark.), Dean Heller Dean Arthur HellerOn The Trail: Democrats plan to hammer Trump on Social Security, Medicare Lobbying World Democrats spend big to put Senate in play MORE (Nev.), Cory Gardner Cory Scott GardnerCook Political Report shifts Colorado Senate race toward Democrat Overnight Health Care: US coronavirus deaths hit 200,000 | Ginsburg's death puts future of ObamaCare at risk | Federal panel delays vote on initial COVID-19 vaccine distribution The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting MORE (Colo.), James Lankford James Paul LankfordMcConnell works to lock down GOP votes for coronavirus bill Charities scramble to plug revenue holes during pandemic Warren calls for Postal Service board members to fire DeJoy or resign MORE (Okla.), Bill Cassidy William (Bill) Morgan CassidyCoushatta tribe begins long road to recovery after Hurricane Laura Senators offer disaster tax relief bill Bottom line MORE (La.) and Rob Portman Robert (Rob) Jones PortmanMcConnell locks down key GOP votes in Supreme Court fight Romney undecided on authorizing subpoenas for GOP Obama-era probes Congress needs to prioritize government digital service delivery MORE (Ohio) signed on to the letter to Sessions.

Trump's immigrant policies have fueled days of media coverage and sparked high-profile backlash from Republicans on and off Capitol Hill.

The senators added in their letter Tuesday that they've "read with increasing alarm" media reports of immigrant children being separated from their parents.

"Although enforcing our immigration laws is an essential responsibility of the federal government, it must be done in a way that is consistent with our values and ordinary human decency," the GOP senators added.

Sessions announced the "zero tolerance" policy in April as part of a move to prosecute adults who illegally cross the border to the fullest extent of the law. As a result, children are separated from their parents and detained as the adults are prosecuted.

Trump and administration officials have tried to shift the blame to Democrats, arguing that their hands are essentially tied.

But GOP senators rejected that in their letter, saying while the current "crisis has multiple contributing causes ... the immediate cause of the crisis is your Department’s recent institution of a 'zero tolerance' policy."

Senators are scrambling to come up with legislation that would deal narrowly with families detained at the border instead of a broader immigration bill like the proposals being debated by the House.

But there is no sign yet of a bill that can get 60 votes in the Senate. Sen. Ted Cruz Rafael (Ted) Edward CruzCruz blocks amended resolution honoring Ginsburg over language about her dying wish Trump argues full Supreme Court needed to settle potential election disputes Press: Notorious RBG vs Notorious GOP MORE (R-Texas) is expected to introduce his own bill and a working group of GOP senators, led by Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (Texas), are aiming to introduce legislation this week.

Meanwhile, Democrats have coalesced behind legislation from Sen. Dianne Feinstein Dianne Emiel FeinsteinFeinstein 'surprised and taken aback' by suggestion she's not up for Supreme Court fight Democrats shoot down talk of expanding Supreme Court Biden leads Trump by 12 points among Catholic voters: poll MORE (D-Calif.) that Republicans believe is too broad and would result in immigrants who tried to enter the country illegally being released.

"Right now there is a full-on Democrat bill, that they've already put out. We'll have some Republican response to it. And then we've got to be able to work together to get an actual final bill that could actually pass," Lankford separately told reporters after a closed-door policy lunch.