"To the Muslim world, we seek a new way forward, based on mutual interest and mutual respect," Mr. Obama said in his speech. He promised to be engaged in world matters and said, "from the grandest capitals to the small village where my father was born: know that America is a friend of each nation and every man, woman, and child who seeks a future of peace and dignity, and that we are ready to lead once more."
But "to those leaders around the globe who seek to sow conflict, or blame their society's ills on the West -- know that your people will judge you on what you can build, not what you destroy," the new president said.
Meanwhile, foreign leaders expressed their support for his presidency throughout the day.
British Prime Minister Gordon Brown, speaking from Downing Street, called Mr. Obama a "man of great vision and moral purpose, he is a man of great determination and energy, and he is a man of great moral purpose," quoted the BBC.
In a statement Israeli Prime Minister Ehud Olmert said, according to CNN: "The greatest democracy in the world has again proven that it is a beacon and example for many countries. The entire State of Israel rejoices with the United States and welcomes President Obama, who took the oath of office this evening. ... We wish the incoming President success in his office and are certain that we will be full partners in advancing peace and stability in the Middle East."
U.N. Secretary-General Ban Ki-moon, who was visiting Gaza following Israel's three-week military campaign against Hamas militants, told reporters: "I sincerely hope that President Obama will take as a matter of priority these Middle East policies."
In addition, Australian Prime Minister Kevin Rudd said: "I believe from everything I have seen, read and heard and from the conversations that I have had with him that the American people have chosen well in their new president," CNN reported.
And Mwai Kibaki, president of Kenya, where Mr. Obama's father was born, said: "On behalf of the government and the people of Kenya and on my own behalf, I extend our message of best wishes on the auspicious occasion of your inauguration as the 44th president of the United States of America.
"On this special day we recall the remarkable journey you have traveled to become the leader of your great country. Through that journey you have inspired many young and old people, not only in America but around the world with a strong message of hope."
Mr. Obama also addressed poor nations and spoke of a changing world from the steps of the Capitol: "To the people of poor nations, we pledge to work alongside you to make your farms flourish and let clean waters flow; to nourish starved bodies and feed hungry minds.
"And to those nations like ours that enjoy relative plenty, we say we can no longer afford indifference to suffering outside our borders; nor can we consume the world's resources without regard to effect. For the world has changed, and we must change with it."