EXETER, N.H./MILFORD, N.H. (Reuters) - U.S. Senator Marco Rubio, emerging from the first presidential nominating contest in Iowa as the leading Republican mainstream contender, portrayed himself in New Hampshire on Tuesday as the party’s best hope to recapture the White House. But Rubio, 44, a U.S. senator from Florida, faces a strong field of establishment rivals in next week’s New Hampshire primary after his stronger-than-expected third-place finish in Iowa behind front-runners Ted Cruz, 45, and Donald Trump, 69. “If I am the nominee, we are going to beat Hillary Clinton and it won’t be by the flip of a coin,” Rubio told supporters in Exeter, New Hampshire, taking a jab at the close Democratic race in Iowa between Clinton and challenger Bernie Sanders, where some precincts were decided on a coin flip. Other more mainstream Republicans including former Florida Governor Jeb Bush, Ohio Governor John Kasich and New Jersey Governor Chris Christie, are expected to do better in New Hampshire than in Iowa and vie with Rubio to become the establishment favorite. Cruz and Trump also headed to New Hampshire as the presidential race shifted to the second nominating contest in the state-by-state battle to pick nominees for the Nov. 8 election to replace Democratic President Barack Obama. Trump told a news conference before a rally in Milford, New Hampshire, that he felt “a tinge” of disappointment at losing to Cruz in Iowa.. The billionaire businessman also picked up an endorsement from former Massachusetts Senator Scott Brown. Cruz told New Hampshire supporters he was like former Republican President Ronald Reagan, urging the state to help ensure his nomination by giving him a win in the Feb. 9 primary.  “Every day from now until Election Day here in New Hampshire, I’m going to continue asking for the men and women of New Hampshire to make that same fateful decision yet again so that we can reignite the promise of America,” Cruz said. Cruz, a conservative U.S. senator from Texas, beat Trump in Iowa’s Republican caucuses with the help of the state’s large bloc of evangelical Christians, but he might struggle to finish on top in New Hampshire, where Republican voters have a more secular and libertarian streak. Cruz apologized to rival Ben Carson over an email his campaign sent on Monday night implying Carson was dropping out of the race and his Iowa backers should switch to Cruz. “This was a mistake from our end, and for that I apologize to Dr. Carson,” Cruz wrote.  The campaign for Carson, who finished fourth in Iowa, said the retired neurosurgeon had accepted Cruz’s apology but that the incident was the sort of “dirty trick” politics that Carson was trying to fight. The Democratic presidential contenders, Clinton and Sanders, also headed to New Hampshire after their close duel in Iowa, where the former secretary of state narrowly edged out the insurgent U.S. senator from Vermont. Vermont borders New Hampshire, and that proximity may give Sanders an advantage in next Tuesday’s primary. Clinton’s razor-thin margin was the smallest in Iowa Democratic caucus history. Concerns about the income gap and economic insecurity have helped Sanders, 74, a self-described democratic socialist who came from far behind in polls to throw a scare into the front-runner in Iowa. Clinton, 68, acknowledged she had to try harder to win younger Democrats, who backed Sanders in Iowa in large numbers. “I’m going to have some work to do to reach out to young voters, maybe first-time voters, who have to make a tough decision,” she told CNN. The two Democrats also renewed a days-old battle over when and where to have more face-to-face debates, and were still talking about potentially meeting in a televised debate on Thursday night in New Hampshire. On the Republican side, U.S. Senator Lindsey Graham of South Carolina, who dropped out of the race in December, said a recent hardening of Rubio’s position on immigration and the strength of his anti-abortion stance might cost him.      “Running to the right to win Iowa is going to be a hard sell here in New Hampshire,” Graham, a supporter of Bush, told Reuters in Rindge, New Hampshire. The son of Cuban immigrants, Rubio said he was the candidate to unite the Republicans in the November election, when the party hopes to regain the White House after Obama’s two four-year terms. “People realized on the Republican side that we cannot afford - this country cannot afford - to lose this election, and that I give the party the best chance not just to unify our party but to grow it,” Rubio told ABC’s “Good Morning America” from Manchester, New Hampshire.   The fluent Spanish speaker hopes to win back some of the Latino vote the party lost in recent years as it toughened its stance on immigration. A foreign policy hawk, Rubio advocates a tough approach to Iran, the Islamic State militant group and other U.S. foes. Iowans who supported Rubio at the caucuses said they responded to his relatively positive message and viewed him as the candidate most likely to beat Clinton should she be the Democratic nominee.    Worries about issues such as immigration and terrorism have fueled the campaigns of Trump and Cruz. Christie on Tuesday accused Cruz and Rubio of lacking executive experience for the job of president. “What do they do exactly in the United States Senate? They talk and they talk. They are not responsible for doing anything,” Christie said at his campaign’s New Hampshire headquarters in Bedford.  Opinion polls of Republicans show Trump leading nationally and in New Hampshire. But the state has a long tradition of bucking trends in presidential primaries. Trump, the outspoken real estate magnate who dominated the Republican race for months, broke an unusual silence of more than 12 hours on Twitter after his defeat in Iowa. “Because I was told I could not do well in Iowa, I spent very little there - a fraction of Cruz & Rubio. Came in a strong second. Great honor,” he wrote on Twitter on Tuesday where he has regularly posted scathing criticism of his opponents.  (Additional reporting by Doina Chiacu, Susan Heavey, Mohammed Zargham and Megan Cassella in Washington, Ginger Gibson and John Whitesides in Iowa; Writing by Alistair Bell and John Whitesides; Editing by Frances Kerry, Howard Goller and Peter Cooney) SAP is the sponsor of this coverage which is independently produced by the staff of Reuters News Agency.