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 HatchOrrin Grant HatchTrump holds more Medal of Freedom ceremonies than predecessors but awards fewer medals Trump to award Medal of Freedom to former Attorney General Edwin Meese Trump to award racing legend Roger Penske with Presidential Medal of Freedom MORE (Utah), sent a letter to Attorney General Jeff SessionsJefferson (Jeff) Beauregard SessionsTrump attacks Sessions: A 'total disaster' and 'an embarrassment to the great state of Alabama' Ocasio-Cortez fires back at Washington Times after story on her 'high-dollar hairdo' Trump's tirades, taunts and threats are damaging our democracy 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 McCainJohn Sidney McCainVideo of fake Trump shooting members of media shown at his Miami resort: report Remembering leaders who put country above party Graham-Trump rollercoaster hits dizzying speed MORE (Ariz.), Pat RobertsCharles (Pat) Patrick RobertsJeffress dismisses evangelical opposition to Trump's Syria decision: Not one will 'switch their vote' Overnight Defense: Trump defends Turkey amid fierce criticism | Senators demand briefing on Syria decision | Turkey confirms strikes on Syrian border | White House says it won't cooperate on impeachment inquiry Pat Robertson 'absolutely appalled' by Trump's Syria announcement MORE (Kan.), Susan CollinsSusan Margaret CollinsFurious Republicans prepare to rebuke Trump on Syria McConnell tightlipped as impeachment furor grows Congress set for showdown with Trump over Kurds MORE (Maine), Lisa MurkowskiLisa Ann MurkowskiMurkowski warns against rushing to conclusions on Trump impeachment GOP requests update on criminal referrals prompted by 2018 Kavanaugh probe Republicans show signs of discomfort in defense of Trump   MORE (Alaska), Bob CorkerRobert (Bob) Phillips CorkerTrump announces, endorses ambassador to Japan's Tennessee Senate bid Meet the key Senate player in GOP fight over Saudi Arabia Trump says he's 'very happy' some GOP senators have 'gone on to greener pastures' MORE (Tenn.), Lamar AlexanderAndrew (Lamar) Lamar AlexanderMcConnell tightlipped as impeachment furor grows GOP senator: 'Inappropriate' to discuss opponents, but impeachment a 'mistake' The revolution has arrived in college admissions MORE (Tenn.), John BoozmanJohn Nichols BoozmanVA chief pressed on efforts to prevent veteran suicides McConnell ups pressure on White House to get a budget deal There is a severe physician shortage and it will only worsen MORE (Ark.), Dean HellerDean Arthur HellerThis week: Barr back in hot seat over Mueller report Trump suggests Heller lost reelection bid because he was 'hostile' during 2016 presidential campaign Trump picks ex-oil lobbyist David Bernhardt for Interior secretary MORE (Nev.), Cory GardnerCory Scott GardnerRepublicans wrestle with impeachment strategy McConnell tightlipped as impeachment furor grows Gardner dodges questions about Trump's call for Biden probe MORE (Colo.), James LankfordJames Paul LankfordMcConnell support for election security funds leaves Dems declaring victory Election security funds passed by Senate seen as welcome first step Senate committee approves 0 million for state election security efforts MORE (Okla.), Bill CassidyWilliam (Bill) Morgan CassidyUN Security Council to meet after Turkey launches Syria offensive Trump faces growing GOP revolt on Syria To win the federal paid family leave debate, allow states to lead the way MORE (La.) and Rob PortmanRobert (Rob) Jones PortmanGOP senator: 'Not appropriate' to ask foreign governments to investigate Biden GOP senator says he doesn't remember signing 2016 letter urging 'reform' of Ukraine prosecutor's office Lobbying World 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 CruzRafael (Ted) Edward CruzCruz: 'Of course' it's not appropriate to ask China to investigate Bidens Sunday Show Preview: Trump's allies and administration defend decision on Syria O'Rourke raises .5 million in third quarter MORE (R-Texas) is expected to introduce his own bill and a working group of GOP senators, led by Sen. John CornynJohn CornynOvernight Health Care — Presented by Coalition Against Surprise Medical Billing — Judge blocks Trump 'public charge' rule | Appeals court skeptical of Trump arguments for Medicaid work requirements | CDC offers guidance for treating vaping-related cases GOP requests update on criminal referrals prompted by 2018 Kavanaugh probe Bottom Line MORE (Texas), are aiming to introduce legislation this week.

Meanwhile, Democrats have coalesced behind legislation from Sen. Dianne FeinsteinDianne Emiel FeinsteinSchiff should consider using RICO framework to organize impeachment We need answers to questions mainstream media won't ask about Democrats The Hill's Morning Report - Trump grapples with Syria fallout 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.