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 HatchHatch warns 'dangerous' idea of court packing could hurt religious liberty Former Democratic aide pleads guilty to doxing GOP senators attending Kavanaugh hearing How do we prevent viral live streaming of New Zealand-style violence? MORE (Utah), sent a letter to Attorney General Jeff SessionsJefferson (Jeff) Beauregard SessionsThe Memo: Mueller's depictions will fuel Trump angst Collins: Mueller report includes 'an unflattering portrayal' of Trump Trump frustrated with aides who talked to Mueller 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 CruzMichael Bennet declared cancer-free, paving way for possible 2020 run Booker, Harris have missed most Senate votes O'Rourke sweeps through Virginia looking to energize campaign MORE (R-Texas) is expected to introduce his own bill and a working group of GOP senators, led by Sen. John CornynJohn Cornyn Embattled senators fill coffers ahead of 2020 Trump struggles to reshape Fed Congress opens door to fraught immigration talks MORE (Texas), are aiming to introduce legislation this week.

Meanwhile, Democrats have coalesced behind legislation from Sen. Dianne FeinsteinDianne Emiel FeinsteinDems reject Barr's offer to view Mueller report with fewer redactions Five takeaways from Mueller's report Only four Dem senators have endorsed 2020 candidates 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.