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 HatchGOP lambasts Trump over performance in Helsinki Senate panel to vote Thursday on Trump's pick to lead IRS Romney: Trump's remarks at Putin summit 'disgraceful and detrimental to democratic principles' MORE (Utah), sent a letter to Attorney General Jeff SessionsJefferson (Jeff) Beauregard SessionsRyan: 'The president must appreciate that Russia is not our ally' Conservatives moving to impeach Rosenstein soon: report Senators urge DOJ to probe whether Russians posed as Islamic extremist hackers to harass US military families 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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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 CruzWisconsin GOP Senate candidate rips his own parents for donations to Dems The Memo: Trump leaves chaos in his wake in UK Beto O'Rourke is dominating Ted Cruz in enthusiasm and fundraising — but he's still headed for defeat MORE (R-Texas) is expected to introduce his own bill and a working group of GOP senators, led by Sen. John CornynJohn CornynMcConnell: Russians are not our friends Russians' indictment casts shadow ahead of Trump-Putin summit Top GOP senator: Trump should be 'clear-eyed' going into meeting with Putin MORE (Texas), are aiming to introduce legislation this week.

Meanwhile, Democrats have coalesced behind legislation from Sen. Dianne FeinsteinDianne Emiel FeinsteinThe Hill's Morning Report — Trump, Putin meet under cloud of Mueller’s Russia indictments Dems launch pressure campaign over migrant families California Dems endorse progressive challenger over Feinstein 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.