The competition between Hillary Clinton and Bernie Sanders entered an urgent new phase Wednesday — a delicate minuet that Clinton and leading Democrats hope will soothe tensions and move their divided party toward enthusiastic unification behind the presumptive presidential nominee.

If all goes well, the Democrats will arrive at their convention in Philadelphia in late July with Sanders fully supportive of Clinton and his millions of fervent followers ready to become foot soldiers in the race against presumptive Republican nominee Donald Trump.

But all that presupposes that Clinton and the senator from Vermont can quickly reconcile. And there was little evidence Wednesday that this would be an easy task.

Clinton said Wednesday that she called Sanders after Tuesday night’s primaries, which secured her the nomination, to congratulate him on what she called “an extraordinary campaign.” She said she admires his determination and highlighted their shared commitment on policy goals like universal health care and rising wages.

“I think he and his supporters understand how much is at stake, that we need to join together to defeat Trump,” Clinton said in an interview with The Washington Post, the first of her 14-month campaign. “And I’m going to really reach out, do everything I can to persuade him. I will be obviously reaching out to his supporters to make that same case.”

On the night six states including California and New Jersey went to the polls, Sen. Bernie Sanders (I-Vt.) vowed to continue "the struggle," even as rival Democratic presidential candidate Hillary Clinton had pivoted to thanking supporters and slamming Republican Donald Trump. (Sarah Parnass/The Washington Post)

Still, Sanders — who digested his new circumstances and discussed a path ahead with advisers and family Wednesday aboard a cross-country flight home to Vermont — has vowed to fight on. He has a rally planned for Thursday evening in Washington ahead of next Tuesday’s District of Columbia primary, the final contest.

On Wednesday, some Sanders backers urged him not to back down until Clinton makes meaningful concessions. “She’s going to have to inspire trust,” said Ben Jealous, a former NAACP leader and a Sanders supporter.

But others, including Sen. Jeff Merkley (D-Ore.) and Rep. Raúl M. Grijalva(D-Ariz.), are gently urging Sanders to accept the reality that Clinton will become the nominee.

A handful of people are playing key roles in trying to broker peace between the two warring campaigns, including President Obama, Vice President Biden, Sen. Elizabeth Warren (D-Mass.) and Senate Minority Leader Harry M. Reid (D-Nev.).

Obama and White House political director David Simas, as well as Warren and Reid, have been in communication with both camps to lay the foundation for an eventual coming together, according to several senior Democrats. Obama called both candidates Tuesday night and was scheduled to meet with Sanders at the White House on Thursday. Sanders also plans to meet with Reid that day on Capitol Hill.

“It’s not a one-way street. They’re both going to have to, in effect, compromise,” Reid said in an interview Tuesday. Reflecting on his earlier career as a trial lawyer, the Senate Democratic leader said, “I never knew what was going to happen when I went to trial, so if I could get a decent offer I would settle that case, and that’s what I think my two friends should take a look at.”

In one way, what Sanders and Clinton will be doing is common at the end of spirited nomination battles. Just eight years ago, Clinton was on the other side as the losing candidate, eventually reaching an accommodation with Obama, but not without some hiccups along the way.

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Leading Democrats say that this time is different and potentially more difficult. For one, Sanders operates outside the Democratic Party structure. He has run in Vermont as an independent and self-described democratic socialist. And although he caucuses with Democrats in the Senate, his ties to the institutional party are decidedly looser than were Clinton’s.

Even more important, however, is that his candidacy — like Obama’s in 2008 — generated great enthusiasm and spawned a powerful grass-roots movement made up of independents and others who do not identify with the Democratic establishment. Clinton will need his voters in the fall, and that no doubt will require the help of Sanders.

How Sanders approaches this period is a source of uncertainty and anxiety.

“He is certainly against Trump and will do anything to stop Trump,” said Tad Devine, a senior strategist for Sanders. “If he is going to get out and endorse her before the convention, how do you do that in a way to persuade as many of his supporters as possible to support her? Not just, ‘I’m for her,’ but, ‘You be for her, too.’ ”

Even though the primary calendar has nearly run out, the Sanders movement is very much alive. He has addressed big, boisterous rallies in California for the past several weeks.

“He’s obviously struggling and in great internal conflict about what’s going on,” said former Vermont governor Howard Dean (D), a Clinton supporter. “He knows intellectually that he can’t win, but he can’t stop himself. . . . There is part of him that doesn’t want to quit.”

Sanders probably will find very little sympathy for the case that he has said he would make between now and the convention, which is to ask the hundreds of superdelegates — Democratic elected officials and party leaders — who have publicly committed to Clinton not only to change their allegiance, but also to go against the total popular vote and the results of state-by-state contests over the past four-plus months.

Even among Sanders’s supporters, that argument may not hold water. Many progressive activists dislike the very concept of superdelegates — a position that Warren, whose liberal base is the same that fueled Sanders’s candidacy, advocated over the weekend.

“I’m a superdelegate and I don’t believe in superdelegates. I don’t think that superdelegates ought to sway the election,” Warren, who has not endorsed a candidate, told reporters in Massachusetts.

Warren’s comment about superdelegates notwithstanding, she is seen by other leaders of the party as uniquely credible and positioned to play one of the most influential roles in bridging the Clinton and Sanders divide.

A Warren adviser, who spoke on the condition of anonymity to speak candidly, said of the senator, “She takes the threat of Trump very seriously and she takes seriously her potential role in helping unify the party.”

One danger is that Sanders could be met by a chorus of Democrats urging him, both personally and publicly, to bow out. “We have to be thoughtful about having a few voices at one time as opposed to everyone talking and preaching at the same time,” said Sen. Robert P. Casey Jr. (D-Pa.), a Clinton backer. “You can’t have 30 people call and start lecturing.”

There is considerable recognition among some party leaders that Sanders deserves deference from Clinton as well as some concessions that would continue to elevate the populist ideas that have been at the heart of his candidacy.

At a meeting Tuesday morning of the Senate Democratic leadership, some senators vented about Sanders vowing to fight on and said that they had lost their patience with him. One Democratic official who relayed the exchange said Reid quieted the chatter, telling his colleagues,“We have to remember that Bernie has always been good to us, he’s always been there when we needed him, and we need to treat him fairly.”

In the interview, Reid, who endorsed Clinton in February, reiterated those feelings and stressed the need to treat both Sanders and his followers respectfully. He said Sanders has been “a tremendously important part of my caucus,” and Democrats would need to “depend on Bernie” for the final seven months of Obama’s presidency.

“A lot of people he has energized and they are rabidly involved in the system now,” Reid said. “What I am so impressed with is that we have these new people, so it’s extremely important that Clinton and Bernie . . . both understand what they’ve got to offer and that they work toward a middle.”

Supporters of Sanders see it as especially crucial that Clinton as well as the Democratic National Committee make genuine concessions. They already have seated five Sanders supporters on the 15-member committee responsible for drafting the party platform in Philadelphia. The committee had its first meeting Wednesday.

Other ideas from Sanders allies include stronger policy positions by Clinton and in the platform on trade, fracking, Social Security, the role of money in politics and other reform issues.

“We’re not talking about little tiny changes,” Merkley said. “My hope and expectation is that Secretary Clinton will find a way to understand how big these issues are and to find that she believes in aggressively taking them on. That would be necessary for the Sanders team to feel like they really want to get out and knock on those doors.”

Some Democrats think that the most important step Clinton could take to bring Sanders’s supporters enthusiastically behind her candidacy — short of naming him as her vice-presidential running-mate — would be to tap Warren for the ticket. The idea has gained currency in Washington in recent weeks.

One potential obstacle is that Massachusetts Gov. Charlie Baker, a Republican, would have the power to fill Warren’s seat in the Senate were Warren to become vice president. But Reid, who has long expressed his admiration for Warren, recently ordered up a legal analysis of Massachusetts election law, first reported by the Boston Globe, which concluded that there are avenues open to the Democrats to minimize the threat.

“I’m a big fan of Elizabeth Warren,” Reid said in the interview. “I would hope that Clinton and Bernie understand what a good woman she is and that they find a role for her, whatever that might be.”

Reid raised the example of Obama in 2008 inviting Clinton into his circle, just as President Abraham Lincoln did in building a team of rivals. “He reached out to her and gave her the best job he had to offer, secretary of state, and I think the history books will recount that was a brilliant move,” he said.

Asked whether he would counsel Clinton to ask Sanders to join her ticket, Reid said he would not give her advice.

“You can make a case for who is the strongest at this stage, either Clinton or Bernie, but the point is they have to work it out,” Reid said. “No one can do it for them.”

Robert Costa, Anne Gearan, Greg Sargent and John Wagner contributed to this report.