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DECORAH, Iowa – Hillary Clinton said on Tuesday that new revenue was needed to shore up Social Security and openly mused about lifting the cap on income subjected to Social Security taxes, a position championed by Senator Bernie Sanders of Vermont.

Asked by a voter at an Iowa campaign event about her plans for Social Security, Mrs. Clinton said: “We do have to extend the life of the trust fund, and that’s going to take some new funding. And I think there are a couple of potential ways of doing it. One is lifting the cap.”

But she did not come out in favor of applying Social Security taxes to all income above the current annual ceiling, $118,500, an idea that is popular with many Democrats and that Mr. Sanders has challenged her to embrace.

Mrs. Clinton has held the position that she would consider Social Security taxes on the wealthiest Americans, saying she might target “some of their income above the current Social Security cap,” according to her campaign website. While she did not make the distinctions about the wealthy or “some” income on Tuesday, a campaign spokesman said her position remains the same as stated on the campaign website.

The site says that to preserve Social Security, “there is no way to accomplish that goal without asking the highest-income Americans to pay more, including options to tax some of their income above the current Social Security cap, and taxing some of their income not currently taken into account by the Social Security system.”