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(CNN) —  

In the wake of the divisive Brett Kavanaugh hearings, Chief Justice John Roberts on Tuesday tried to assure the public that the US Supreme Court serves the whole country, not one political party over another, and that it is committed to collegiality.

Yet, irrespective of what is happening in the political branches, America’s highest court is deeply split along ideological and political lines, and Roberts sometimes fosters that divide.

“Those of us on the court know that the best way to do our job is to work together in a collegial way,” Roberts said at the University of Minnesota Law School. “I am not talking about mere civility, although that helps. I am instead talking about a shared commitment to a genuine exchange of ideas and views through each step of the decision process. We need to know at each step that we are in this together.”

That message is sometimes belied by the court’s rulings and by personal tensions among the nine. In the most recently completed term, October 2017 to June 2018, many major rulings broke along 5-4 lines, with the five conservatives led by Roberts in control and the four liberals in dissent. The five on the right were appointed by Republican presidents, the four on the left by Democratic presidents.

The chief justice wrote for the narrow majority in the incendiary case of Trump v. Hawaii, upholding the administration’s travel restrictions on people from mostly Muslim countries. The same five conservatives also voted together, over protests from the four liberals, to reverse a four-decade court precedent involving non-member fees for labor union collective bargaining.

President Donald Trump immediately applauded the decision, saying on Twitter, “Big loss for the coffers of the Democrats!”

On a less partisan, more personal level, while the justices put up a polite front, some of them recount testiness behind the scenes. Roberts in public venues typically exudes respect for his colleagues, yet in the private confines of the columned building, he can sometimes be dismissive. Friction surfaced on occasion during the last annual session between senior liberal Ruth Bader Ginsburg and Neil Gorsuch, Trump’s first appointee, and in an instance between Roberts and liberal Stephen Breyer.

The latter occurred in a February case testing a police officer’s right against self-incrimination as Breyer began asking the officer’s lawyer specifics about testimony at a preliminary hearing, Roberts admonished Breyer not to go beyond the record in the case. Breyer said he wanted to determine whether there was even a true Fifth Amendment issue before the court to resolve. (The justices often quarrel about raising potentially unreliable information outside the record of the case, although most, including Roberts, have occasionally done it.)

But this time Roberts said, “As far as I’m concerned, coming in and saying I want to know about this thing that’s not in the record is no different from somebody else coming off the street and saying: Hey, wait a minute, I know what happened in this case.” Roberts declared he would “discount the answers” to Breyer’s questions. Three months later, the justices dismissed the case, City of Hays v. Vogt, without a decision.

From the start of his 13-year tenure, Roberts has tried to put the judiciary on a higher plane than the two political branches, accentuating that the justices are not elected and have lifetime tenure.

After the Senate approved Gorsuch in April 2017, filling a vacancy that had lasted more than a year because Republicans blocked then-President Barack Obama’s choice of Judge Merrick Garland, Roberts told a group at Rensselaer Polytechnic Institute in Troy, New York: “First, I want to point out one thing. Throughout this whole process, the Supreme Court has been quietly going about its business of deciding the cases before it, according to the Constitution, in a completely non-partisan way. … We in the judiciary do not do our business in a partisan, ideological manner.”

The recent Kavanaugh hearings, in which the nominee accused his critics of a partisan smear as he faced accusations of sexual assault in his teenage years, may have prompted the chief justice to speak out more forcefully.

As he took the stage in Minnesota on Tuesday, Roberts first referred to “the contentious events in Washington of recent weeks” and emphasized the court’s independence from the executive and legislative branches. “I will not criticize the political branches. We do that often enough in our opinions. But what I would like to do, briefly, is emphasize how the judicial branch is – how it must be – very different.”

During his four-minute prologue, Roberts cited decades-old landmarks, including Brown v. Board of Education, rejecting “separate but equal” schools, as signs of the high court’s independence.

In equal measure, Roberts touted the justices’ efforts at collegiality. The 63-year-old Roberts referred to the justices’ century-old tradition of shaking hands before they hear oral arguments or meet in private sessions to decide cases.

“It’s a small thing, perhaps, but it is a repeated reminder that, as our newest colleague put it,” Roberts said, implicitly referring to Kavanaugh, “we do not sit on opposite sides of an aisle, we do not caucus in separate rooms, we do not serve one party or one interest. We serve one nation. And I want to assure all of you that we will continue to do that to the best of our abilities, whether times are calm or contentious.”