With the Democratic mayoral primary out of the way, candidates are shifting their attention to November's general election. 

Queens Assemblyman Zohran Mamdani spoke with CBS News New York Thursday about his strategy for attracting independent voters. 

He said he sees his resounding success in the mayoral primary as a mandate to deliver on the Democratic socialist platform he campaigned on. 

"The support from New Yorkers, just in this first round, we received more votes than Eric Adams did in total in 2021, and it shows a mandate to deliver a city that New Yorkers can actually afford," he said. 

Zohran Mamdani's campaign promises and tax plan

Mamdani's platform includes proposals like city-owned grocery stores and free buses, along with free child care for every New Yorker aged 6 weeks-5 years. He also says he wants to freeze the rent for stabilized units. 

Mamdani says he will pay for his campaign proposals by raising the corporate tax and taxing top earners a flat 2%.

Gov. Kathy Hochul has other plans. She is up for re-election herself next year. 

"I have said that I will not raise income taxes on the people of our state," Hochul said.

So what's Mamdani's strategy for delivering on his promises when critics say a mayor doesn't have the authority to fulfill them?

"Building the movement that brought us to this point," Mamdani said. "Ultimately, it's a sign of a different kind of politics, and I'm already hearing from colleagues in the state legislature, their excitement on delivering back to working people, and I know that there's a hunger for these very proposals."

So how does he plan to reach those independent voters, or ones who shy away from the word "socialism"?

"You know, we won a number of neighborhoods that Donald Trump won," Mamdani said. "And yet, we won them by focusing on a message of affordability, because it is a message that binds all New Yorkers. And I've actually found that it's just as compelling to independents and Republicans as it is to Democrats." 

"Ultimately, I'm confident of winning this race"

Mamdani said he's spoken with Democratic leaders from across the country, including Sen. Charles Schumer and Rep. Hakeem Jeffries. So what does he think the future of the Democratic party should look like?

"I think it should look like anyone who is focused on working people. Because ultimately that was what made me proud to become a Democrat, and so many Americans feel the same way, and yet for quite a while have felt as though we've left our roots, we've left our focus, and it's time to come back to that," Mamdani said.

Mamdani said he appreciated former Gov. Andrew Cuomo's congratulatory call on primary election night. 

"I told him what I've told New Yorkers since, which is that my focus is in bringing our party back together, and leading this entire city, no matter whether a New Yorker voted for me, or voted for Governor Cuomo, or didn't vote at all out of frustration of a broken political system. I am going to represent them, and I want to lead them too," Mamdani said.

Cuomo says he's weighing his options for running as an independent. This comes as Mayor Eric Adams officially launched his campaign Thursday as an independent. 

So does Mamdani want Cuomo to run in the general election as an independent, since Cuomo may split votes with Adams?

"Ultimately, I'm confident of winning this race no matter who's running in it, because what we've seen is that we're bringing people back to the Democratic party, and we're stitching together a coalition that Eric Adams himself had in 2021. But we're going beyond it, and we're going to actually deliver for that coalition, as opposed to betray them in the manner that he has," Mamdani said. 

Adams takes aim at Mamdani

Adams is already taking shots at Mamdani's progressive platform. 

"This is not a city where you use idealism to state you're giving everything to everyone for free. There's no dignity in someone giving you everything for free. There's dignity in giving you a job," Adams said.

Hours after launching his reelection campaign, Adams appeared on the Don Lemon Show, where Lemon asked if Adams thought Mamdani was "an antisemite."

"Yes, I do. I think some of the comments of, you know, you look at some of his rap lyrics where he's talked about his embracing of Hamas. That says a lot," Adams said.

A campaign spokesperson sent CBS News New York the following statement in response: "These are the lies of a failed Mayor, desperately trying to scare and divide us in order to distract from his record of scandal and corruption. Zohran will be a Mayor who represents and protects every single New Yorker across the five boroughs, tackling the issue of antisemitism with action, not rhetoric, and delivering a city everyone can afford."

• Zohran Mamdani