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Hillary Rodham Clinton had planned to focus her remarks Wednesday at a Politics and Eggs breakfast in Manchester, N.H., in support of the politically fraught, if somewhat arcane, issue of the Export-Import Bank and how it helps small businesses in the United States.

But a voter’s question about the death penalty pushed Mrs. Clinton to confront the heated issue for the first time in the Democratic nominating contest.

Asked her position on capital punishment, Mrs. Clinton said she did not support abolishing the death penalty, but she did encourage the federal government to rethink it.

“We have a lot of evidence now that the death penalty has been too frequently applied, and too often in a discriminatory way,” she said. “So I think we have to take a hard look at it.”

Mrs. Clinton added, “I do not favor abolishing it, however, because I do think there are certain egregious cases that still deserve the consideration of the death penalty, but I’d like to see those be very limited and rare, as opposed to what we’ve seen in most states.”

Her statement immediately ignited an outcry from some liberals who hoped she would have taken a tougher stance against the death penalty. Mrs. Clinton’s two main Democratic rivals, Senator Bernie Sanders and Martin O’Malley, have called to abolish the death penalty.

“The death penalty is racially biased, ineffective deterrent to crime, and we must abolish it,” Mr. O’Malley said in a statement.

Mrs. Clinton expressed support for the death penalty when she ran for the Senate in 2000. Her husband, Bill, expanded the use of capital punishment as president by signing the 1994 federal crime bill, parts of which Mrs. Clinton denounced this spring in the first major policy speech of her 2016 campaign. In that speech, she called for an end to the era of mass incarceration and for improved relations between African-Americans and mostly white police forces, but she did not wade deeply into the death penalty.

Until Wednesday, the topic had not come up in the Democratic contest, but botched attempts at lethal injection in several states have put the issue back in the spotlight. Mrs. Clinton recently campaigned in Florida, Texas and Virginia, three of the top states in executions since 1976.