In last year's re-election, Klobuchar carried counties that voted for Trump in 2016.
The list of Democrats already in the race features several better-known senators with the ability to raise huge amounts of money.
Klobuchar, 58, is the fifth Senate Democrat to join the race, and the fifth woman serving in Congress to announce a bid.
She is citing the need to "heal the heart of our democracy and renew our commitment to the common good".
"For every American, I'm running for you", she told an exuberant, snow-covered crowd gathered Sunday at a park along the Mississippi River with the Minneapolis skyline in the background.
"Senator Klobuchar loves her staff - they are the reason she has gotten to where she is today".
For example, while she has publicly spoken out against President Trump's immigration and border policies, she has not voiced her support for the movement to abolish US Immigration and Customs Enforcement (ICE).
The primary field soon could expand to include prominent Democrats such as former Vice-President Joe Biden and Vermont Senator Bernie Sanders.
Some Democratic operatives in early states believe the reports could undercut her public image.
"For too long, leaders in Washington have sat on the sidelines while others try to figure out what to do about the changing economy and its impact on our lives, what to do about the disruptive nature of new technologies, income inequality, the political and geographical divides, the changing climate, the tumult in our world", she said.
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Klobuchar initiated the campaign by singing the national anthem. The span was built after the previous bridge collapsed in 2007, killing 13 people.
The announcement came days after national media outlets published stories casting Klobuchar as a boss who was overly tough on staff members who shared their stories anonymously.
Klobuchar began her foray into Minnesota politics by advocating for better access to health care for babies and new mothers after her own daughter was born with health complications, a personal narrative she is likely to use in the debate about the future of the nation's health care system.
"We are exhausted of the shutdowns and the showdowns, the gridlock and the grandstanding", she told the crowd and a national audience on TV.
"We've got the opportunity to replace chaos with courage".
"She's a very popular U.S. Senator who's really effective at passing legislation", Olson said Sunday.
But her legislative record has drawn criticism from both the GOP and some fellow Democrats. Recently, she pushed for Senate investigations into whether Facebook Inc. broke the law when it resisted oversight on how Russians used its platform to meddle in the 2016 presidential election.
Minnesota Republican Party Chairwoman Jennifer Carnahan said Klobuchar lacks the clout of political heavyweight senators like Paul Wellstone and Rudy Boschwitz and she raised questions about Klobuchar's stances on key issues. "I am asking you to join this campaign".
Unruffled, Klobuchar continued as Kavanaugh asked again. It also chronicled challenges including her father's struggle with alcoholism, a topic she touched on during Kavanaugh's Senate hearing, and her parents' divorce. Several former aides have been quoted saying she is hard to work for, with bouts of "explosive rage" leading to exceptionally high staff turnover. "I was truly trying to get to the bottom of the facts and the evidence".