Obama made a reference to gun control, saying that the nation needed to ensure that "all our children, from the streets of Detroit to the hills of Appalachia to the quiet lanes of Newtown, know that they are cared for, and cherished, and always safe from harm."
However, congressional Republicans and some Democrats, as well as the powerful gun lobby, have rejected proposals Obama recently announced in response to the Connecticut school shootings that killed 20 Newtown first-graders last month.
In citing climate change as a priority, Obama raised the profile of the issue on the national agenda after a presidential campaign in which it was almost never mentioned.
"We will respond to the threat of climate change, knowing that the failure to do so would betray our children and future generations," he said, warning of a "long and sometimes difficult" path to sustainable energy sources in a nation dominated by its fossil fuel industries such as oil and coal.
"America cannot resist this transition; we must lead it," Obama said. "We cannot cede to other nations the technology that will power new jobs and new industries -- we must claim its promise."
Obama infused his speech with references to two assassinated American icons -- President Abraham Lincoln and civil rights leader Martin Luther King Jr.
In one passage, Obama cited "blood drawn by lash and blood drawn by sword" in mentioning the Civil War and slavery. It mimicked Lincoln's second inaugural address in 1865, when he spoke of the possibility that "every drop of blood drawn with the lash shall be paid by another drawn the sword."
Of King, Obama referred to those who came to Washington almost 50 years ago "to hear a preacher say that we cannot walk alone; to hear a King proclaim that our individual freedom is inextricably bound to the freedom of every soul on Earth."
The inauguration coincided with the national holiday honoring King.
The president concluded by urging Americans to fulfill their responsibility as citizens by meeting "the obligation to shape the debates of our time -- not only with the votes we cast, but with the voices we lift in defense of our most ancient values and enduring ideals."
At a little more than 2,100 words, Obama's speech was about 300 shorter than his first inaugural address four years earlier.
In 2009, he was fresh off his historic election as the nation's first African-American president, facing an economic recession, wars in Iraq and Afghanistan and the ongoing terrorist threat.
This time, he could cite progress in his first term -- economic recover, the end of one war and winding down of the other -- while offering a broader prescription for expanding opportunity and justice to all Americans, in keeping with the nation's founding principles.
David Maraniss, author of the book "Barack Obama: The Story," said the difference from four years ago was palpable, adding: "I could feel his heart beating this time."