New York, Colorado and Massachusetts have ended cooperation with a White House initiative to deploy the National Guard to the US-Mexico border.
Massachusetts has assets at the border already, which will return. The other states have cancelled future deployments.
President Trump announced the deployment in April as part of his administration's "zero-tolerance" policy.
Families have been separated at the border, with thousands of children separated from their parents.
Three US states have cancelled agreements to send members of the National Guard to the US-Mexico border as part of a backlash over the Trump administration's policy of separating migrant families trying to enter the US.
The governors of New York, Colorado, and Massachusetts are now refusing to send state troops to the US-Mexico border.
Massachusetts, which had already sent resources south, is now withdrawing them. The other two cancelled plans to do so.
Charlie Baker, the Republican governor of Massachusetts, called the administration's policy "cruel and inhumane," becoming the latest in a string of Republican figures to criticise the president.
He said Monday that "we told the National Guard to hold steady and to not go down to the border — period," according to NBC 10 Boston. "We won't be supporting that initiative unless they change the policy."
Gov. Baker had made the decision to deploy troops earlier this month, following a proclamation signed by Trump in April that ordered National Guard troops to help protect the US-Mexico border.
Andrew Cuomo, Democratic governor for New York, said: "In the face of this ongoing tragedy, let me be very clear: New York will not be party to this inhumane treatment of immigrant families.
"We will not deploy National Guard to the border, and we will not be complicit in a political agenda that governs by fear and division."
In the face of the federal government’s inhumane treatment of immigrant families, New York will not deploy National Guard to the border. We will not be complicit in this ongoing human tragedy. pic.twitter.com/a2tTzjNisR
— Andrew Cuomo (@NYGovCuomo) June 18, 2018
Cuomo called on the Acting Inspector General of the Department of Homeland Security to investigate "illegal and discriminatory" tactics by the Immigration and Customs Enforcement agency and "to tell us what his office is doing about the assault on immigrant families along our border."
In an executive order on Monday, John Hickenlooper, Democratic governor for Colorado, barred state resources from being used to separate immigrant families.
"The state of Colorado is a safe and welcoming place for all its residents, regardless of immigration status," the order reads.
"To maintain public confidence in the integrity of state government and promote trust and cooperation betweens state and local law enforcement and all Colorado communities, I issue this Executive Order to forbid any state agency from using any state resources for the purpose of separating any child from his or her parent or legal guardian on the sole ground that such parent or legal guardian is present in the United States in violation of federal immigration laws."
In an additional statement on Monday, Gov. Hickenlooper called on the Trump administration to reverse the practice of family separation.
“We urge the administration to stop this cruel practice. If the White House won’t act, Congress should. No political end is worth destroying families and traumatizing children.”
— Governor Jared Polis (@GovofCO) June 18, 2018
More than 2,300 children have been separated from this parents since April, when the Trump administration launched its zero-tolerance policy.
Children had been separated from their families under previous administrations, but the practice has accelerated under the zero tolerance regime.