Photo Courtesy: The United Nations

(CBS News) Striking a hopeful but serious tone about the future of the Middle East, President Obama at the United Nations General Assembly on Tuesday called on his international counterparts to directly and honestly confront the sources of unrest in Muslim countries, as well as the tensions between the West and the Arab world.

At the same time, he urged world leaders -- and, no doubt, an American electorate -- to "remember that this is a season of progress."

Mr. Obama hailed the political progress in Tunisia, Egypt and Libya, as well as developments outside the Arab world, as in Somalia and Burma.

"Around the globe, people are making their voices heard, insisting on their innate dignity, and the right to determine their future," he said. "And yet the turmoil of recent weeks reminds us that the path to democracy does not end with the casting of a ballot."

Beginning and ending his nearly hour-long remarks by invoking the memory of U.S. Ambassador Chris Stevens, who was murdered along with three other Americans when the U.S. compound in Benghazi, Libya came under attack, the president laid out the values that America stands for -- the values Mr. Obama said the nation would continue to promote around the world.

"We believe that freedom and self-determination are not unique to one culture," the president said. "These are not simply American values or Western values - they are universal values. And even as there will be huge challenges that come with a transition to democracy, I am convinced that ultimately government of the people, by the people and for the people is more likely to bring about the stability, prosperity, and individual opportunity that serve as a basis for peace in our world."

Mr. Obama touted the United States' support for the different democratic movements that unfolded throughout the Middle East over the past two years, glossing over inconsistencies in the level of support his administration showed for protesters. He noted that the U.S. "insisted on change" in Egypt and was "inspired by the Tunisian protests that toppled a dictator," while failing to mention the United States' lack of support for pro-democracy protesters in Bahrain.

Mr. Obama said, "Just as we cannot solve every problem in the world, the United States has not, and will not, seek to dictate the outcome of democratic transitions abroad, and we do not expect other nations to agree with us on every issue."

Nevertheless, the president declared, "America will never retreat from the world."

Mr. Obama's remarks came just a day after his presidential opponent Mitt Romney charged that the United States' international influence has waned under Mr. Obama's leadership. The president's speech was his last international address before Election Day, and he used the opportunity to highlight ways in which he's advanced American interests on the international stage.

"It is because of the progress I've witnessed that after nearly four years as president, I am hopeful about the world we live in," Mr. Obama said. "The war in Iraq is over, and our troops have come home. We have begun a transition in Afghanistan, and America and our allies will end our war on schedule in 2014. Al Qaeda has been weakened and Osama bin Laden is no more."