Washington CNN  — 

Maryland Sen. Barbara Mikulski, the longest-serving woman in the history of Congress, said that the Democratic primary ends in June, adding her voice to the growing calls in the party to unite behind one candidate ahead of the July convention.

In an interview with CNN, Mikulski was careful not to call on Sen. Bernie Sanders, who is trailing front-runner Hillary Clinton, to quit.

“I’m not one of those people (to say), ‘Tell Bernie to get out,’ ” she said.

But she made clear that after the final votes are counted in June, the primary is “over,” breaking with Sanders, who has vowed to take his fight to the July convention in Philadelphia.

“I’m a supporter of the full process playing out. I know it’s hard. I know it’s a slog … but I want to be sure that all 50 states, territories, Democrats abroad – that everybody has their say,” said Mikulski, who supports Hillary Clinton. “So when we go to the convention, everybody’s spoken. But when the process is over, through either primary or caucus, then it’s over.”

Asked if she thought Sanders should quit in June, Mikulski said: “My feeling is follow the rules … What I’m saying is that the process is established by each state, and territories and Democrats abroad, play out, and then when that’s over, that’s over.”

In the aftermath of the chaos in Nevada state party convention on Saturday, a growing number of Democrats have grown fearful that if Sanders continues his candidacy, it could provoke a tumultuous and ugly party convention in July, giving presumptive Republican nominee Donald Trump a leg up headed into the general election.

Some Democrats, including Sen. Dianne Feinstein of California, want Sanders to step aside after the votes are done in mid-June, given that he very likely will be trailing Clinton in pledged and superdelegates at that time.

By pledging his full support to Clinton, Democrats say, it would give the party time to heal and unify in the fight against Trump. Yet other top Democrats, including Senate Minority Leader Harry Reid, have so far refused to call on Sanders to quit in June, worried that a heavy hand could backfire with the Vermont senator’s legions of supporters.

Unlike other senators, Mikulski wouldn’t criticize Sanders’ handling of the Nevada episode, but suggested he should do more.

“Well I would like Bernie to be Bernie. I admire Bernie’s in many ways, and particularly his advocacy for nonviolence, the principles of one Dr. King and others … but he needs to reaffirm his own belief of that principle and to encourage his volunteers and supporters to follow the same,” she said.

Asked if Sanders should speak out more forecefully, Mikulski added: “I think he knows that Bernie should be Bernie, in the full-throated way that Bernie can. One thing we know: when Bernie’s ready to speak, you’ll hear him.”