WASHINGTON – President Bush last night tried to shore up support for his proposal to overhaul Social Security, saying he would endorse a policy to increase benefits for lower-income Americans in his push to make the system solvent.

In the second press conference of his second term, Mr. Bush touted his plan for voluntary private accounts for younger workers and said the program should “protect those who depend on Social Security the most” by having benefits for lower-income workers grow faster than those for wealthier workers.

“By providing more generous benefits for low-income retirees, we’ll make this commitment,” the president said.

In foreign policy, Mr. Bush said he warned the new Iraqi prime minister yesterday against “politicizing the military,” a sign the White House is committed to keeping in place an officer corps recruited in large part from the ranks of the old Baathist military.

Mr. Bush also pledged that America would not send suspected terrorists to countries that admitted to torture practices. “We operate within the law, and we send people to countries where they say they’re not going to torture the people,” he said.

Responding to Americans’ concern about rising gas prices, Mr. Bush said there would be “no price gouging at gas pumps in America,” and he called on Congress to approve energy legislation by the summer.

Yesterday’s press conference marked the end of the president’s 60-day cross-country tour of American cities to push his plan for private individual accounts. Democrats and some Republicans in Congress are vehemently opposed to the president’s proposal to allow younger workers to divert part of their Social Security taxes into accounts that would be invested in the stock market.

The chairman of the Senate Finance Committee, Senator Grassley, a Republican of Iowa, said earlier this week that he intends to introduce a compromise Social Security bill by July. There is bipartisan support for addressing the long-term solvency of the massive entitlement.

When asked whether he would consider it a success if Congress forwarded to him legislation that addressed the solvency of Social Security without including an option for voluntary savings accounts, Mr. Bush said, “I feel strongly that there needs to be voluntary personal savings accounts as a part of the Social Security system. I mean, it’s got be a part of the comprehensive package.”

The president has said the system will go bankrupt by 2041, and that by 2017 the Social Security program will pay more benefits than it collects in taxes.

Despite his strong support for the voluntary accounts, the president also said he was open to ideas from both parties on reforming the massive entitlement program. “A variety of options are available to solve the rest of the problem, and I will work with Congress on any good faith-proposal that does not raise the payroll tax rate or harm our economy,” he said.

The White House’s case for Social Security reform could be hindered because Congress is so divided over the president’s judicial nominees and his choice to represent America at the United Nations.

Earlier this week, Senate Majority Leader Frist, a Republican from Tennessee, took part in a Christian rally whose speakers charged that Democrats were opposed to the president’s judicial nominees because of their religious faith.

When asked whether Democrats are opposed to the judges because of their faith, Mr. Bush said “No, I just don’t agree with it … I think people oppose my nominees because of judicial philosophy.”

The president also defended John Bolton, his nominee to be America’s ambassador to the United Nations, who has been the subject of a contentious nomination process as Democrats have investigated charges that he punished lower-ranking bureaucrats who disagreed with him on intelligence matters.

Mr. Bush, calling Mr. Bolton “a blunt guy,” said he personally asked Mr. Bolton before he was nominated whether he thought the United Nations was important. The nominee answered in the affirmative, according to the president.

“John Bolton can get the job done at the United Nations,” the president said. “Seemed like to me it made sense to put somebody who’s capable, smart, served our country for 20 years, been confirmed by the United States Senate four times, and who isn’t afraid to speak his mind, in the post of the ambassador to the U.N.”

The president said he invited Iraq’s new prime minister, Ibrahim al-Jaafari, to Washington and urged him to reach out to disaffected parties. He said his message to Mr. al-Jaafari, who has promised to pursue a rigorous de-Ba’athification process of the military and security services, was to “keep stability.”

“Don’t disrupt the training that has gone on. Don’t politicize your military, in other words. Have them there to help secure the people,” Mr. Bush said he told Mr. al-Jaafari.

The president expressed displeasure with Russia’s president, Vladimir Putin, for selling anti-aircraft missiles to Syria. “We didn’t appreciate that,” Mr. Bush said, “But we made ourselves clear.” The two leaders are scheduled to meet in Moscow next month.

The president said he did not know if North Korea possessed the capability of mounting a nuclear warhead on a missile, as the head of the Defense Intelligence Agency testified before Congress yesterday. But Mr. Bush did say that he was operating under the assumption that North Korea’s leader, Kim Jong Il, did have that capability, which is one reason why he instructed the Pentagon to develop a missile defense system.

“Perhaps Kim Jong Il has got the capacity to launch a weapon, and wouldn’t it be nice to be able to shoot it down?” the president asked rhetorically.

Senators Clinton and Levin, a Democrat of Michigan, yesterday wrote a letter to Secretary of State Rice urging her to conduct bilateral negotiations with Pyongyang.

“It is important to include our allies and friends in Northeast Asia in our diplomatic effort, but this does not mean that we cannot hold bilateral talks with North Korea,” the two lawmakers wrote.

The president yesterday repeated his commitment to approach Mr. Kim, a man he said starved his people and built “concentration camps,” through the six-party talks. He also said America would not unilaterally take North Korea’s violations of the nuclear nonproliferation treaty to the U.N. Security Council.

Noting that Ms. Rice recently proposed the Security Council option, the president said, “Obviously, that’s going to require, you know, the parties agreeing.”