The Obama administration said it would drop a plan to tax so-called 529 college savings accounts, after the proposal sparked widespread criticism over its potential impact on the middle class.

The move followed a public call by House Speaker John Boehner (R., Ohio) on Tuesday for the White House to withdraw its plan. Calls also were coming privately from leaders of the president’s own party. House Minority Leader Nancy Pelosi (D., Calif.) pressed the case for dropping the plan in conversations with senior administration officials aboard Air Force One, as she flew with the president from India to Saudi Arabia, according to a person familiar with the matter.

A White House official said late Tuesday: “Given it has become such a distraction, we’re not going to ask Congress to pass the 529 provision.”

Ahead of last week’s State of the Union address, Mr. Obama proposed a set of tax changes aimed at boosting incomes for low- and middle-income households, including expanded availability of a break known as the American Opportunity Tax Credit, which provides as much as $2,500 per student for higher-education expenses. To offset the cost of those plans, the White House plan would have narrowed or ended several other breaks, including tax-free distributions from 529 accounts, which disproportionately benefit higher-income households, according to administration officials.

The administration said it will continue to push for expanded tax credits for higher-education costs, as well as other breaks for lower- and middle-income households.