“In the face of the federal government’s inhumane treatment of immigrant families, New York will not deploy National Guard to the border,” Cuomo said on Twitter.

Later, Cuomo said that the state was preparing to sue the Trump administration over the policy.

Cuomo directed three state agencies to sue over the policy, which has led to at least 2,000 children being separated from their families, including more than 70 who are being housed in federal facilities in New York, the governor’s office said Tuesday.

The suit will be filed in coming weeks, Cuomo said in a telephone call with reporters.

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US President Donald Trump defended the policy on Tuesday, saying it was the only effective way to fight illegal immigration.

Trump announced plans in April to send thousands of National Guard troops to the border, where they could remain until the wall he pledged to build is constructed.

Larry Hogan, the Republican governor of Maryland, said he would not send any National Guard resources to the border “until this policy of separating children from their families has been rescinded.”

Hogan said he had ordered a four-member helicopter crew, which had been stationed in the border state of New Mexico, to “immediately return” home.

“Immigration enforcement efforts should focus on criminals, not separating innocent children from their families,” Hogan said.

Delaware Governor John Carney, a Democrat, posted on Twitter that “given what we know about the policies currently in effect at the border, I can’t in good conscience send Delawareans to help with that mission”.

Virginia Governor Ralph Northam, a Democrat, said he had ordered the recall of a helicopter and four soldiers from the state National Guard from the border state of Arizona.

“When Virginia deployed these resources to the border, we expected that they would play a role in preventing criminals, drug runners and other threats to our security from crossing into the United States – not supporting a policy of arresting families and separating children from their parents,” Northam said.

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John Hickenlooper, the Democratic governor of Colorado, signed an executive order on Monday that forbids the use of state resources “for the purpose of separating any child from his or her parent or legal guardian”, a practice he called “cruel and un-American”.

Roy Cooper, the Democratic governor of North Carolina, decried the “cruel policy of tearing children away from their parents” and said he was recalling the three National Guard officers who had been deployed to the area.

Massachusetts Governor Charlie Baker, a Republican, said that the policy was “cruel and inhumane,” and that a National Guard helicopter crew which had been scheduled to go to the border later this month would not be deployed.

And Rhode Island Governor Gina Raimondo, a Democrat, said she would not send National Guard units to the southern border “to support family separation”.

The Trump administration is facing condemnation at home and abroad for the separations, the product of a “zero tolerance” policy on undocumented migrants.

US officials say more than 2,300 children have been separated from their parents or guardians since early May, when the policy was announced.

Additional reporting by Bloomberg.