The relationship between Governor Andrew Cuomo and Mayor Bill de Blasio took another nose dive Tuesday as they engaged in a new round of public sniping over homelessness and bipartisan cooperation. NY1's Grace Rauh filed the following report.

Governor Andrew Cuomo works closely with Republican lawmakers in Albany but says he wouldn't stand beside his one-time gubernatorial rival, Westchester County Executive Rob Astorino, the way Mayor Bill de Blasio did on Tuesday. De Blasio and Astorino appeared together in Penn Station to call for more federal transportation funding.

"The Republican who I ran against, this is a man who is against the woman’s right to choose. This is a man who wants to lock refugees out of this country. It is not a person who I would stand next to," Cuomo said.

That swipe is the latest example of the bitter feud between the mayor and governor, both Democrats. And it did not stop there. The governor also criticized the mayor for the city's growing homeless problem. The mayor has said the state needs to kick in more funding to help people get back on their feet.

"To me, it’s not just the money. It’s more managing the city properly, efficiently, effectively, smartly, especially on this issue, which causes so much pain to people," Cuomo said.

The mayor and Astorino fired back.

"There is no litmus test we take before we agree to get transportation funding for our communities," de Blasio said.

"It seems like the governor has some insecurities. and since he is a constituent of mine, I'd be more than happy to set him up with our Department of Community Mental Health," Astorino said.

On homelessness, the mayor says the governor is not looking at the facts.

Meanwhile, the mayor is trying to make some headway on another issue that has troubled his administration: horse-drawn carriages. As a candidate, he promised to get rid of the horse carriages. Now, sources tell NY1, he is trying to negotiate a compromise to reduce the number allowed in the city and restrict them to Central Park.