NEW YORK — Two real-life Grinches posed as police to push inside a couple’s home and steal their valuables and holiday presents on Christmas Eve while their young children slept, prosecutors said Monday.

The men wore bulletproof vests bearing the New York Police Department logo and claimed to have a warrant when they approached Robert Kapovic, the Queens district attorney’s office said.

They pushed their way into Kapovic’s home in the Whitestone neighborhood and forced him and his wife upstairs, where they tied them up for nearly four hours while ransacking the home, prosecutors said.

“They acted like the Grinch in the Dr. Seuss classic ’How the Grinch Stole Christmas,”’ District Attorney Richard A. Brown said in a statement. “Unfortunately for them their plan was foiled when real police officers stopped them and the victims’ belongings were returned in time for the holiday.”

Kapovic was pistol-whipped, and his wife was pushed around and threatened with the prospect of never seeing her children again, prosecutors said.

The youngsters — ages 7, 3, 2 and 1 — apparently slept through the incident, even as the attackers rifled through their bedrooms and took $4,000 cash, diamond jewelry, electronics and liquor from throughout the home, they said.

When the men left in the early hours of Dec. 24, the couple freed themselves, and Kapovic followed them in his car, using his onboard global positioning system to lead police to them, prosecutors said.

Authorities said they recovered the stolen property, police paraphernalia and two pellet guns.

Constantino Christo and Nicholas Papaleo pleaded not guilty at their arraignment on charges including burglary, robbery, assault, criminal impersonation and endangering the welfare of a child.

Papaleo, 33, was held without bail, and Christo, 43, was ordered held on $1 million bail.

Lawyers for the Brooklyn residents, who each could face up to 25 years in prison if convicted, did not immediately return telephone calls seeking comment Monday.