WASHINGTON – President Bush will not insist that personal retirement accounts be included in any Social Security reform passed by Congress, a senior White House aide indicated yesterday.

In a round of television appearances following Friday’s presidential press conference, the White House chief of staff, Andrew Card, emphasized the president’s openness and flexibility in reaching a bipartisan compromise to put the fraying entitlement program on a path to permanent solvency.

Mr. Bush has also not ruled out the possibility of subjecting a higher portion of workers’ incomes to Social Security taxes, said Mr. Card, keeping alive a policy option that is supported by some Democrats but strongly opposed by many of the president’s backers.

Meanwhile, Mr. Bush this week plans to continue traveling around the country promoting the case for Social Security reform. Tomorrow, he is scheduled to address workers at a Nissan manufacturing plant in Canton, Miss. On Wednesday, he will address Social Security before the Latino Coalition’s Small Business Conference in Washington.

In his press conference on Friday, Mr. Bush said the private accounts have “got to be a part of a comprehensive package.” Democrats responded by saying a bipartisan deal could not be reached as long as Republicans insist on diverting some Social Security taxes into private accounts.

But Mr. Card, who made the rounds of television morning shows yesterday, suggested the president was open to compromise.

“We want to work with the legislative process,” Mr. Card said, when asked whether the president would veto legislation that did not include accounts, during his appearance on NBC’s “Meet the Press.”

Mr. Card said the president’s only requirement for a solution is that the Social Security tax rate of 12.4% not be increased. However, he said the president has not ruled out raising the upper limit on income to which the tax applies, above the current $90,000 cap.

“He has said it’s all on the table. If Congress wants to consider it, he’ll take a look at it. It might not be the president’s preference,” Mr. Card said on CNN’s “Late Edition.”

On Friday, Mr. Bush outlined a proposal to slow the rate growth of benefits for future retirees, with greater reductions for middle- and upper-income earners. Mr. Card said the idea was merely one proposal, but not a deal-breaker.

“There is going to have to be some adjustment of benefits. … He wants Congress to consider the proposal, among other things,” he told CNN.

Democrats as well as some Republicans panned the proposal, known as “progressive indexation,” yesterday because it would mean reductions from scheduled benefits for workers earning as little as $30,000 or less by some estimates.

“I don’t think families that earn $30,000 are rich, and I don’t think they ought to have their benefits cut,” said Senator Levin, a Democrat of Michigan, on CNN.

The minority leader in the House, Rep. Nancy Pelosi of California, called the proposal “an assault on the middle class.”

“I don’t know what the middle class ever did to President Bush, but he has it in for them,” she said on ABC News’s “This Week.” Ms. Pelosi said the first step in Social Security reform should be paying back the money borrowed by the federal government from the program’s trust fund.

Democrats favor “a bipartisan solution with modest changes,” said Mr. Levin.

But Senator Coleman, a Republican of Minnesota, said Democrats are failing to put forward their own solutions to the fiscal problems created as the baby boom generation retires. “You have yet to hear what my colleagues on the other side of the aisle are for, only what they are against,” Mr. Coleman said. “That is not going to fix anything.”

Some criticism of the president’s benefits proposal also came from Republicans.

A former presidential hopeful, Steve Forbes, who ran on a platform advocating a flat tax, said the indexation proposal was a “mistake.”

“If you start means-testing Social Security, you will turn it into a welfare system and undermine popular support for it,” Mr. Forbes, a publisher, said on CNN. And raising the cap on taxable earnings would be “a wimp policy,” he said.

“Raising taxes is not going to strengthen the economy. You’re going to hurt small businesses and hurt job creation,” said Mr. Forbes, who supports private accounts.

Meanwhile, the former labor secretary in the Clinton administration, Robert Reich, praised Mr. Bush for adopting what he called a “progressive approach.”

“If someone is going to have to sacrifice in the future … better that those cuts occur on the people who can afford them, rather than on the poor,” Mr. Reich said.

But he said the estimated reductions in benefit growth would reach too far down the income scale. “The president is cutting way down into the middle class, and that is the problem with the proposal,” said Mr. Reich, who advocated raising the cap on taxable earnings to $120,000, or apply a 2% or 3% surtax on incomes over $90,000.

Mr. Forbes warned that Republicans should insist on accounts, refuse to raise taxes, and trust that voters would blame Democrats for any failure to reach a deal.

“I would rather have nothing done and take it to the American people in 2006,” he said. “The idea they have to slash benefits or raise taxes is preposterous.