(CNN) Former Rhode Island Gov. Lincoln Chafee said Thursday on CNN that he's running for the Democratic nomination for president, just a week after announcing he formed an exploratory committee, his most definitive statement he's made toward formalizing a 2016 campaign.

"Yes, that's why I'm running. Because I feel strong about where we're going as a country," Chafee told CNN's "New Day" on Thursday, when asked why he's been so critical of Democratic front-runner Hillary Clinton. Chafee was asked by CNN's John Berman in the context of having not formally declared his presidential campaign.

Chafee spokeswoman Debbie Rich said Chafee did not declare himself as a candidate for president Thursday, despite saying "that's why I'm running."

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"We are still in the exploratory committee phase," she told CNN in a phone interview, adding, "We will file the proper papers to be an official candidate, but that has not happened yet."

Chafee, a former Republican and former senator, announced he was forming an exploratory committee last week . Chafee's been differentiating himself from fellow Democratic primary contenders by taking sharp jabs at Clinton, willing to be more critical than would-be challengers former Maryland Gov. Martin O'Malley or former Virginia Sen. Jim Webb over her vote in Congress to authorize the war in Iraq.

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