But, she said, she needs to become the nominee quickly so that she can direct all of her focus on Republicans.
Clinton did not mention Wyoming during her remarks, but her aides boasted publicly about splitting delegates with Sanders in the Cowboy State, something they did not think they would do going into the contest.
"We are on a path to the nomination, but I need to win big here in New York, because the sooner I can become the nominee, I can turn and unify the Democratic Party like I did with President Obama in 2008," Clinton said. "And the sooner we can go after the Republicans full-time."
The race between Clinton and Sanders has grown more acrimonious in the past week, with the Vermont senator saying the former secretary of state was not qualified
to be president before walking back his comments.
Clinton, while ahead of Sanders in delegates, has had to fight off questions about the Vermont senator's momentum now that he has won eight of the last nine contests. Clinton has publicly said before that she would like to start focusing more on Republicans like Donald Trump and Ted Cruz.
"I look forward to debating whoever emerges as the Republican nominee, because both of them have really put anti-immigration statements at the core of their campaigns," Clinton said Saturday. "Donald Trump started this campaign calling immigrants rapists and criminals and he has gone on from there."
Clinton has campaigned consistently in New York for the last week, making stops around the city and upstate in Buffalo, Rochester and Albany. Clinton, who represented the state in the U.S. Senate for eight years, has said this primary is personal for her.
She stopped by Junior's, a cheesecake shop before her rally in Brooklyn, where she shook hands with patrons and chatted with Rep. Hakeem Jeffries, a Democrats who represents parts of Brooklyn and Queens.
Although a waiter served Clinton three pieces of cheesecake -- original, strawberry and pineapple -- Clinton declined to take a bite with the press present.
"I learned early on not to eat in front of all of you," she said when asked by a reporter her how the cake was. "So I am sitting here just pining, pining for a bite."
New York, although comfortable for Clinton personally, has presented her campaign with a tightrope to walk: How to talk about her position on the minimum wage in the midst of the Empire State raising its state minimum to $15.
Clinton has supported raising the federal minimum wage to $12 for much of her campaign while also supporting states such as New York and California and cities like Seattle, which have enacted higher minimum wages.
But on Saturday, Clinton appeared to indicate that she wanted a $15 federal minimum wage.
"I am very proud of New York and I was with (Gov. Andrew) Cuomo when he signed the bill raising the minimum wage in New York," Clinton said. "We now gotta do that for the entire nation."
This is different than what Clinton usually says. On Friday in New York, Clinton said, "I want to do everything I can to make sure (New York's minimum wage) works and to raise it at the federal level."
Nick Merrill, Clinton's traveling press secretary, said Clinton did not misspeak and her statement reflected her articulating her desire to "raise the federal minimum wage nationally to $12" while she also "remains supportive of local efforts to go to $15 on the state and local level, and wants to see that happen beyond New York, California and Seattle and the handful of other places that are phasing it in already."
Clinton, who appeared with Cuomo on Monday, the day he signed the bill, said earlier on Saturday that the way New York pass a the minimum wage is an example of "how a piece of consequential legislation actually gets passed."