Donald Trump Says He's 'Honored' to Lead GOP After More Primary Wins

— -- Presumptive Republican presidential nominee Donald Trump thanked his supporters Tuesday night for giving him the "honor" to lead the Republican Party, following his projected wins in New Jersey, New Mexico,and South Dakota. Later in the evening, he was named the projected winner of Montana and California, sweeping all five states holding primaries Tuesday.

"You've given me the honor to lead the Republican Party this fall," Trump said tonight at the Trump National Golf Club in Briarcliff Manor, New York, where he entered to the song "We Are The Champions."

Acknowledging his role as the party's presumptive nominee, he said, "Tonight we close one chapter in history, and we begin another ... We're going to lead the Republican Party to victory this fall."

He has battled with others in his party the last few days, and he seemed acknowledge some of their concerns. "I understand the responsibility of carrying the mantle, and I will never, ever let you down," he told the 300 people assembled at the venue. "Too much work, too many people, blood sweat and tears, never going to let you down."

"I will make you proud of our party and our movement," he said. His theme of unity follows some dissent among Republican senators and representatives, including House Speaker Paul Ryan, who rebuked Trump for his criticism of Judge Gonzalo Curiel, and one senator who retracted his support for Trump today.

Trump released a long statement today that did not apologize for his comments and that continued to question Curiel's impartiality.

But after a firestorm of denunciation from top Republicans like Ryan, Trump took a decidedly measured tone Tuesday night, reading his short statement from a teleprompter — something that he has roundly criticized rival Hillary Clinton for doing. He purposefully did not address any of his comments regarding Curiel, taking no questions from reporters gathered.

On uniting those who voted for other Republican candidates, Trump said repeatedly that he "will work very hard to earn that support."

And he made a direct plea to Bernie Sanders supporters. "To all of those Bernie Sanders voters who have been left out in the cold by a rigged system of superdelegates, we welcome you with open arms," Trump said. "We can't fix the rigged system by relying on very — and I mean this so, so strongly — on the very people who rigged it, and they rigged it and do not ever think anything differently."

He continued, "We can't solve our problems by counting on the politicians who created our problems. The Clintons have turned the politics of personal enrichment into an art form for themselves."

In taking the podium, flanked by his wife, Melania Trump, four children and their spouses, Donald Trump avoided his usual fiery rhetoric; tonight he spoke of immigration without mentioning the wall he has said he would build between the U.S. and Mexico. He has taken up the term "America first," using the phrase to mean ensuring safety and security while pushing his key issues of business and immigration reform.

"Better hope I'm president," Trump said as he wrapped up.

He teased a "major speech" next week in which he said he would be discussing Bill and Hillary Clinton.

"I think you're going to find it very informative and very, very interesting," Trump said.

He closed out his victory speech by saying, "The beauty of America first is that it brings us all together. Every American worker of every background is entitled to the same benefits, protections and rights and privileges. It's got to be that way.”