Mayor Bill de Blasio said Wednesday he won't apologize for past remarks that antagonized some police officers, but he pledged to address "valid issues," raised by cops and he harshly criticized the rhetoric of the most extreme anti-NYPD protesters as "sick."

De Blasio's remarks came as Gov. Andrew M. Cuomo met privately at his Manhattan office with police union leaders to try to heal their divisions with de Blasio, calling the rift "a distraction we don't need."

"Everyone in New York City knows this situation is unsustainable," Cuomo told reporters during an appearance later at Hofstra University. "We see on the TV terrorism is alive and well and growing. This city and this state is a possible terrorist target," Cuomo said.

De Blasio said he can't take back remarks he made voicing empathy with New Yorkers who were upset when a Staten Island grand jury last month decided not to charge a police officer in the death of Eric Garner by an apparent chokehold.

Union leaders, including Patrolmen's Benevolent Association President Patrick Lynch, were particularly incensed when de Blasio recalled coaching his biracial son, Dante, to be cautious around cops.

"You can't apologize for your fundamental beliefs," de Blasio said at an unrelated news conference in the Bronx.

But other comments by the mayor Wednesday suggested a deliberate shift in tone. Unprompted, he laced into protesters who direct hateful comments at cops.

Anti-brutality demonstrations are set to resume Thursday after a lull in the aftermath of the Dec. 20 killings of two police officers. The mayor called out sponsoring groups that have "a long history of, unfortunately, allowing some of their members to say really inappropriate, reprehensible things about our police officers -- things that I think are actually quite sick, anything that suggests violence towards police."

A City Hall official said the mayor was referring to groups such as OWS-S17, Occu-Evolve and Peoples Power Assemblies. Messages left with the groups were not immediately returned.

When he was asked at a Dec. 22 news conference about such protesters, de Blasio scolded reporters. "What you managed to do is pull up the few who do not represent the majority, who are saying unacceptable things," de Blasio said then.

Asked Wednesday about reported dissension within the PBA -- with some cops saying their top need is more equipment and protective gear, not a de Blasio apology -- the mayor said, "It's a big, diverse police force with lots of different viewpoints." He added, "What's most important is that we, in government, listen to those opinions, and figure out what we can do about the real valid issues that come up."

Last week, when police unions last week had suggested Cuomo as possible mediator, de Blasio and Police Commissioner William Bratton were cool to the idea. Cuomo said his involvement was not, by his definition, a mediation.

"I am working, meeting with everyone, talking to everyone, to resolve those problems," Cuomo said. "That is different than 'I feel like this, you feel like that and let's talk about how we feel.' "

With Robert Brodsky