Some Republicans said they searched in vain for olive branches. Sen. John McCain (R-Ariz.), who lost to Obama in 2008, said the president did not reach out to "those on the other side of the aisle in a plea to work together."
"That's his privilege, but I note that was not in the speech," McCain told reporters.
Sen. Jeff Sessions (R-Ala.) said Obama's speech was "not too political" under the circumstances.
"I would just say that at this point in history it's fair for us to ask, 'Can't we make the government leaner, more productive and less costly, and allow the vitality of America to flourish in the private sector?'" he said.
There was no official estimate of the crowd size. In 2009, an estimated 1.8 million people attended Obama's first inauguration, a record. Monday's throng did not extend to some areas that were occupied last time. Ridership on Washington's transit system was down by more than a third from four years ago, according to the transit agency.
Also missing at the sequel were some of the lofty ambitions of his first inaugural address, reflecting, in part, first-term setbacks at home and overseas.
When Obama first assumed office, he reached out to America's enemies and spoke of a "new way forward" to the Muslim world. His second inaugural address was much more inward looking, and offered little more than a fleeting reference to "engagement" with overseas foes and alliances with friends.
According to White House aides, Obama wanted to emphasize equality and opportunity in his second inaugural speech. "It was deeply emotional and personal," one aide said.
Obama decided in December to use his inaugural address and upcoming State of the Union speech as a package — a "one-two punch," in the words of one advisor.
Monday's address was meant to highlight second-term priorities and frame the argument he will take to the public when he appears before a joint session of Congress on Feb. 12, Lincoln's birthday. At that point the administration will unveil more details.
"He wants to leave office with the economy restored in such a way that the middle class really can be thriving," said a senior advisor, who requested anonymity to talk about internal planning. "The other issues are all part of how you get there. Immigration is part of it. Investment in education. Every piece is about how we can be pushing the arc of progress a little farther along."
Those on the National Mall clearly approved of Obama's speech. They cheered his promise to respond to the threat of climate change, to expand equality for women and gays, and to make it easier for voters to cast ballots without waiting hours in line.
Throughout the day, campaign supporters received emails from Obama, inviting them to join a tax-exempt advocacy group that his political network has formed to push his agenda. The president's advisors hope the group can help sway support in Congress for Obama's policies, many of which face opposition in the Republican-led House and uncertain fates in the Democratic Senate.
"America's possibilities are limitless, for we possess all the qualities that this world without boundaries demands: youth and drive; diversity and openness; an endless capacity for risk and a gift for reinvention," Obama said. "My fellow Americans, we are made for this moment, and we will seize it — so long as we seize it together."
Kathleen Hennessey, Lisa Mascaro and Michael A. Memoli in the Washington bureau contributed to this report.