Democratic 2020 presidential hopeful Elizabeth Warren announced in an interview on Saturday that she wants to break up not only Amazon, Google, and Facebook, but also Apple -- as the Massachusetts senator pushes further to the left of her numerous Democratic rivals on a host of populist issues.

Speaking to The Verge at the South by Southwest (SXSW) technology conference in Austin, Texas, Warren specifically demanded that Apple must be forced to either surrender control over the App Store, or cease selling its own apps within it.

"Apple, you’ve got to break it apart from their App Store. It’s got to be one or the other," Warren said. "Either they run the platform or they play in the store. They don’t get to do both at the same time."

She elaborated: "If you run a platform where others come to sell, then you don’t get to sell your own items on the platform because you have two comparative advantages. One, you’ve sucked up information about every buyer and every seller before you’ve made a decision about what you’re going to to sell. And second, you have the capacity — because you run the platform — to prefer your product over anyone else’s product. It gives an enormous comparative advantage to the platform."

Warren asserted that similar antitrust principles were "applied to railroad companies more than a hundred years ago," and that "we need to now look at those tech platforms the same way."

Responding to a federal appeals court's recent rejection of the Trump Justice Department's bid to block the planned AT&T-Time Warner merger, Warren told The Verge: "How well do I think the Justice Department and the FTC are doing? Not well at all, and not well for a long time now."

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In a lengthy post on the website Medium on Friday, Warren targeted Amazon, Facebook, and Google for breakup, but did not mention Apple.

Warren said the large tech giants had used mergers to "limit competition," citing examples such as Facebook's acquisitions of Instagram and WhatsApp; Amazon using its market power to "force" smaller competitors, such as Diapers.com to sell to the company; and Google buying mapping company Waze and advertising company DoubleClick.

She also mentioned that their marketplaces were used to limit competition. "Amazon crushes small companies by copying the goods they sell on the Amazon Marketplace and then selling its own branded version. Google allegedly snuffed out a competing small search engine by demoting its content on its search algorithm, and it has favored its own restaurant ratings over those of Yelp," Warren wrote.

Warren, who specifically denied being a Socialist as recently as this weekend, proposed two ways of restoring competition to the tech sector, including passing legislation that would designate the large platforms as "platform utilities" and reversing already approved mergers, which she deemed "illegal and anti-competitive."

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Rob Atkinson, president of the Information Technology and Innovation Foundation (ITIF), a think tank for science and technology policy, sharply disagreed with Warren's proposal.

"The Warren campaign’s call to break up big tech companies reflects a 'big is bad, small is beautiful' ideology run amok," Atkinson said in a statement obtained by Fox News. "The proposal ignores the fact that many of the services big tech companies now provide free used to cost consumers money. Breaking up large Internet companies just because they are large won’t help consumers. It will hurt them by reducing convenience, reducing quality of service and innovation, and in some cases leading to the introduction of priced services."

"Breaking up large Internet companies just because they are large won’t help consumers." — ITIF president Rob Atkinson

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Warren herself tempered some of her rhetoric on Saturday, saying simply, "I am not" when asked if she considered herself a democratic Socialist, in the vein of New York Rep. Alexandria Ocasio-Cortez or Vermont Sen. Bernie Sanders.

“All I can tell you is what I believe – there’s an enormous amount to be gained from markets. Markets create opportunities. … but markets have to have rules. They have to have a cop on the beat,” Warren told an energetic crowd at the Austin City Limits’ Moody Theater.

Warren's calls for major changes in antitrust law follow her other relatively radical proposals, including her idea of taxing idle wealth. Specifically, Warren has proposed an annual 2 percent tax on every dollar of net worth above $50 million and a 3 percent tax on every dollar of net worth above $1 billion.

But because Warren would seek to tax wealth itself -- as opposed to income or some other kind of transfer -- without equally apportioning such a tax among the states, legal experts say it is likely unconstitutional.

Warren has also said that Native Americans should be “part of the conversation” on reparations for African-Americans -- a move that threatens to bring back her own history with Native Americans.

Her fellow 2020 hopefuls Sen. Kamala Harris, D-Calif., and former San Antonio Mayor Julian Castro have come out in favor of reparations for African Americans, but have so far not gone as far as Warren in opening the door to reparations for Native Americans.

Fox News' Chris Ciaccia and Adam Shaw contributed to this report.