WINDHAM, N.H. — Senator Bernie Sanders and former secretary of state Hillary Clinton escalated their verbal wrangling Wednesday, sharply questioning each other’s liberal credentials in perhaps the most acrimonious day of their fight for the Democratic nomination.

The two conducted their dispute digitally, with posts aimed at their millions of Twitter followers, and then appeared separately in a CNN sponsored town hall meeting Wednesday night.

During the televised event at the Derry Opera House, Sanders charged that Clinton could not claim to be both progressive and moderate, prompting Clinton to question his validity as a “gatekeeper’’ of the left.

Sanders, in his volley of tweets, called attention to her more “moderate’’ positions on a host of issues important to the party’s liberal base, including her vote to authorize the war in Iraq, ambivalence about the Keystone XL Pipeline, and support for an early draft of the Trans-Pacific Partnership.

“You can be a moderate,’’ Sanders said in one tweet. “You can be a progressive. But you cannot be a moderate and a progressive.’’

Clinton has since said the Iraq vote war was a mistake, and she no longer supports the pipeline or the TPP agreement.

Clinton’s campaign responded Wednesday afternoon in its own series of tweets defending her record and attacking Sanders.

“This shouldn’t be a debate about who gets to define ‘progressive’ — it should be about who will get real results for American families,’’ stated the first tweet.

“Now, if you do want to make it about who’s a ‘real progressive,’?’’ @BernieSanders, what were you on these days?’’ read the next tweet, which included a graphic that listed several of Sanders’ votes, including those against tighter gun control.

The feud underscored a divided Democratic Party, with longtime Clinton allies springing to her defense and questioning Sanders’ standingto define progressivism. On the other side, Sanders backers rallied behind the self-described democratic socialist.

Appearing first during the two-hour CNN show, Sanders reiterated his doubts about Clinton’s progressive credentials, after offering praise for her work while in office and insisting he wants to run a positive campaign.

Sanders said he considered himself a Democrat and cited his years caucusing with Democrats in both the House and Senate and serving as ranking member on the Senate Budget Committee and former chairman of the Veterans’ Affairs Committee.

He also turned a question about polls showing that Clinton is viewed as the more capable candidate on national security issues to contrast his 2002 House vote against authorizing military force in Iraq with Clinton’s Senate vote to support it.

With Sanders still onstage, Clinton’s campaign circulated critiques of his tax and health care plan, which would raise middle-class taxes. By contrast, Clinton would shift the burden to high-income earners, aides said.

Her campaign also contrasted Clinton’s experience and frequent invocations of foreign policy topics since she launched her bid with Sanders’ “lack of engagement,’’ arguing that he had “all but ignored foreign policy on the campaign trail.’’

Following Sanders onstage, Clinton said her Iraq vote was a “mistake’’ but added she thought it would permit the Bush administration to apply leverage against Saddam Hussein rather than trigger a rush to war.

Clinton said she and Sanders “share the same big progressive goals,’’ but disagree on the means of achieving them.

“I’m a progressive who likes to get things done. And I was somewhat amused today that Senator Sanders has set himself up as the gatekeeper of who’s a progressive,’’ Clinton said, adding that under his rubric President Obama, Vice President Joe Biden, and the late senator Paul Wellstone would not qualify.

When moderator Anderson Cooper asked her if she needed to be paid $675,000 for three speeches to the investment bank Goldman Sachs after she left the State Department, Clinton replied, “I don’t know, that’s what they offered.’’

Republicans jumped on the remark via social media as tone deaf. But Clinton told Cooper that Wall Street has failed to alter her policy positions. “Name anything they’ve influenced me on. Just name one thing,’’ she challenged.

On Tuesday in Keene, in response to a reporter’s question about whether he believed Clinton is a progressive, Sanders replied, “Some days, yes. Except when she announces she is a proud moderate. Then, I guess, she is not a progressive.’’

Clinton, campaigning in Derry on Wednesday, called Sanders’ jab “kind of a low blow’’ and pointed to a litany of achievements, like securing health care for children and blocking the privatization of Social Security.

Sanders denied that labeling Clinton a “moderate’’ was a negative attack.

Concerns about Clinton’s popularity on the left have helped fuel Sanders’ appeal. Clinton’s rise to political prominence came as the Democratic Party was shifting to the center.

That repositioning left her vulnerable to Barack Obama in 2008, when he capitalized on the party’s move back to the left during President George W. Bush’s administration.

Clinton supporters have said they are concerned she could be susceptible to a similar insurgency this year, but they also worry about the damage to her in a general election if she moves too far left.

Wednesday’s town hall marked the first joint appearance of the narrowing Democratic field. Former Maryland governor Martin O’Malley suspended his campaign after a poor showing in Iowa.

The Democratic National Committee announced four additional debates on Wednesday, including a face-to-face debate in Durham on Thursday night.

Annie Linskey of the Globe Staff contributed to this report. Jim O’Sullivan can be reached at jim.osullivan@globe.com. Follow him on Twitter @JOSreports.