(CNN) President-elect Donald Trump is facing the prospect of a first major fight over the shape of his White House, less than a week into his transition.

The announcement Sunday that Trump campaign CEO and "alt-right" media chief Steve Bannon would serve as chief strategist and senior counsel to the new President set off alarm bells among civil rights and anti-extremist groups, who are now calling on Trump to withdraw Bannon's appointment.

Bannon and Republican National Committee chairman Reince Priebus had emerged as the finalists for the chief of staff position, considered one of the most powerful in any White House. The job ultimately went to Priebus, a decision that some initially took as an indication Trump planned to govern more moderately than he had campaigned. But Bannon's twin role quickly undermined that narrative -- and set off a groundswell of outside pressure.

"Steve and Reince are highly qualified leaders who worked well together on our campaign and led us to a historic victory," Trump said in a Sunday afternoon press release. "Now I will have them both with me in the White House as we work to make America great again."

But by the early evening, the backlash had begun to grow. Here is a running tab of the groups lining up to oppose Bannon.

The Southern Poverty Law Center

"What this signals is Donald Trump bringing hatred of immigrants and Muslims, and misogyny directly into the White House," Mark Potok, a senior fellow at the Southern Poverty Law Center told CNN on Monday. "It is a disaster."

In a broader attack Sunday, SPLC President Richard Cohen underlined Bannon's close ties to the "alt-right," a loose association of right-wing trolls and white nationalists who operate mostly online and have proliferated on Twitter, where they routinely harass women and minorities.

"In his victory speech, Trump pledged to be the president for 'all Americans' and to 'bind the wounds of division' in our country, " Cohen said. "Appointing someone like Bannon, who will have the president-elect's ear every single day, makes a mockery of that pledge."

The Anti-Defamation League and J Street

The Anti-Defamation League CEO Jonathan Greenblatt tweeted a statement saying it was "a sad day when a man who presided over the premier website of the 'alt right' -- a loose-knit group of white nationalists and unabashed anti-Semites and racists -- is slated to be a senior staff member in the 'people's house.'"

J Street, a progressive pro-Israel group, also called on Trump to "rescind this appointment immediately."

The decision, they said in a statement, "gives the many groups that Bannon and Breitbart have targeted -- from women to Muslims, from Latino immigrants to African-Americans, from LGBT people to conservative Republican Jews who oppose the 'alt-right' -- legitimate reason to fear that their rights may be threatened by a Trump administration."

The Council on American-Islamic Relations

The Council on American-Islamic Relations also asked that Trump reject Bannon, calling his elevation to a powerful White House role a "disturbing message that anti-Muslim conspiracy theories and White nationalist ideology will be welcome in the White House."

"We urge President-elect Trump to reconsider this ill-advised appointment if he truly seeks to unite Americans," said CAIR National Executive Director Nihad Awad.

People For the American Way

As the tensions escalated Monday, People For the American Way President Michael Keegan joined the chorus contesting Bannon's new role, and called on the Capitol Hill GOP to join.

"Congressional Republicans need to stand up and call out Trump for choosing Bannon as a senior adviser and 'equal partner' to Trump's chief of staff," he said. "This isn't about partisan politics; no one with Bannon's record should be anywhere near the White House."

IfNotNow and other liberal organizers and activists

While the powerful American Israel Public Affairs Committee, or AIPAC, would not weigh in, citing "a long-standing policy of not taking positions on presidential appointments," smaller Jewish groups registered their concern.

"The Bannon appointment is a signal to the Jewish community that we are not safe in a Trump administration," Yonah Lieberman, an organizer with IfNotNow told CNN. "This is a clear sign that they will not be friendly toward to the Jewish community and a direct threat to our allies, including Muslims and people of color."

AllOfUs, another progressive millennial activist group, also weighed in.

"Steve Bannon is an anti-Semite and out fascist, and his appointment to one of the most powerful positions in the White House is an incredibly dangerous indication of where is our democracy headed," organizer Max Berger told CNN. "Trump has made various extreme statements during the campaign and his appointment of a white supremacist nationalist to be his chief strategist is an indication of just how extreme he would be as president."

Rebecca Katz, a former top aide to Reid and New York Mayor Bill de Blasio, said Trump's pick was a "horrendous error in judgment," but also further evidence of a lowered standard for this president-elect.

"Donald Trump has a white nationalist who will be just steps away from the Oval Office," she told CNN. "And no one is asking him to apologize because no one expects him to."

Congressional Democrats

The office of Minority Leader Harry Reid, the outgoing Nevada Senator, said Trump's choice of Bannon to serve as a co-equal to Priebus indicated that "White Supremacists will be represented at the highest levels in Trump's White House."

Top House Democrat Nancy Pelosi echoed Reid, saying in a statement that the hire was a sign that Trump had no plans to divert from the "hateful and divisive vision that defined his campaign."

"There must be no sugarcoating the reality that a white nationalist has been named chief strategist for the Trump administration," she said.

Oregon Sen. Jeff Merkley, a Democrat, also called on Trump to pull back Bannon's appointment.

"After running a campaign built on inciting divisions and hate, Donald Trump has claimed he wants to unite America," he said in a statement. "Yet he has done nothing meaningful to stop the wave of hate crimes and hate speech he has unleashed, and now has brought that strategy right into the Oval Office."

Later Monday, Sen. Ron Wyden, another Oregon Democrat, tweeted his opposition

"Steve Bannon ran a website that trafficked in anti-Semitism & misogyny," Wyden wrote. "He is an unacceptable choice to advise a U.S. president."

Steve Bannon ran a website that trafficked in anti-Semitism & misogyny. He is an unacceptable choice to advise a U.S. president. — Ron Wyden (@RonWyden) November 14, 2016

Democrats also got a boost from an independent who ran for their presidential nomination and has emerged as one of the party's most vocal leaders. Sen. Bernie Sanders warned on Monday that Bannon's appointment "should make us very nervous."

"We're going to tell him and Trump that we will stand together and not be divided up," Sanders tweeted.

Steve Bannon's appointment should make us very nervous. We're going to tell him and Trump that we will stand together and not be divided up. — Bernie Sanders (@SenSanders) November 14, 2016

The Trump campaign responds

On Monday, Trump campaign manager Kellyanne Conway responded to the criticism in comments to the press at Trump Tower in New York City.

"(Bannon) has got a Harvard business degree. He's a Naval officer. He has success in entertainment. I don't know if you're aware of that. And he certainly was a Goldman Sachs managing partner," Conway said, seeming to echo another Trump ally, Newt Gingrich, who on Sunday argued that Bannon could not be anti-Semitic because he worked in Hollywood and with Goldman Sachs.

Asked if she was concerned by his work with the alt-right, Conway said, "I'm personally offended that you think I would manage a campaign where that would be one of the going philosophies. It was not."

"It is easy to see why the KKK views Trump as their champion when Trump appoints one of the foremost peddlers of White Supremacist themes and rhetoric as his top aide," Reid spokesman Adam Jentleson said in a statement that included links to stories published on Breitbart News, the media empire Bannon presided over before taking leave to join the Trump campaign as its CEO in August.

Among the headlines: "Birth Control Makes Women Unattractive and Crazy" and "Bill Kristol, Renegade Jew," a broadside against the conservative commentator and Weekly Standard editor, a Republican who refused to support Trump.