New York Gov. Andrew Cuomo will go to Cuba … but North Carolina is off-limits.

What gives?

That’s the charge being leveled against the Democratic governor by North Carolina Gov. Pat McCrory’s office after Cuomo banned certain official travel to the Tar Heel State over a law critics say discriminates against transgender people.

Earlier this week, Cuomo signed an executive order barring “non-essential state travel” to North Carolina. He required all state agencies to “immediately review” any such requested trips, adding: “As long as there is a law in North Carolina that creates the grounds for discrimination against LGBT people, I am barring non-essential state travel to that state.”

But McCrory spokesman Josh Ellis accused Cuomo of “hypocrisy and demagoguery.” In a statement, he noted that Cuomo last year visited Cuba, a country he said has a "deplorable" human rights record.

He also questioned whether the Democrat would ask the Syracuse University basketball team to boycott the upcoming Final Four because it is hosted by Houston, where voters last year defeated a non-discrimination ordinance. (As a private university, Syracuse would not be subject to a state travel ban even if one existed.)

The retort heightens the war of words between the two state governments, as North Carolina faces increasing pressure from other states and companies as well over the new law.

The law, which McCrory signed last week, would prevent local governments from protecting people on the basis of sexual orientation and gender identity when they use public accommodations such as hotels and restaurants. People also would have to use multi-stall bathrooms that match their birth certificates at state agencies and public schools and universities.

Critics, even inside the state government, say this would discriminate against transgender people.

Attorney General Roy Cooper, the governor's Democratic challenger in the looming election, announced Tuesday that his office won't defend this "national embarrassment" against a federal lawsuit filed by two transgender men, a lesbian law professor and civil rights groups.

McCrory complained this week that a well-coordinated national campaign is "distorting the truth," and in a video Tuesday accused Cooper of "inventing conflict that simply doesn't exist" to justify his argument to refuse to defend the law.

Cuomo’s trip to Cuba last year was part of a two-day trade mission with other state industry leaders. It preceded President Obama’s historic visit last week to Havana, where he was joined by congressional lawmakers of both parties.

A Cuomo spokesman, in response to Ellis, told there is a “fundamental difference between legislative action that strips LGBT people of their rights and taking affirmative steps to help change long standing practices in a foreign country.”

The Associated Press contributed to this report.