BERLIN, Germany (CNN) -- Standing before a massive crowd in a city that once symbolized division, Sen. Barack Obama warned Thursday about the dangers of allowing new walls to come between the United States and its allies.

"People of the world, look at Berlin, where a wall came down, a continent came together, and history proved that there is no challenge too great for a world that stands as one," Obama said at Berlin's Victory Column in the Tiergarten park.

"The fall of the Berlin Wall brought new hope. But that very closeness has given rise to new dangers, dangers that cannot be contained within the borders of a country or by the distance of an ocean," he said.

Obama said that people of all nations must stand together to face challenges of the 21st century, from terrorism to global warming to genocide.

"We cannot afford to be divided. No one nation, no matter how large or powerful, can defeat such challenges alone. None of us can deny these threats or escape responsibility in meeting them," he said.

The greatest danger, Obama said, "is to allow new walls to divide us from one another." Read a transcript of the speech

Obama called on Europeans and Americans to join to "defeat terror and dry up the well of extremism that supports it." Watch Obama call for unity »

"If we could win a battle of ideas against the communists, we can stand with the vast majority of Muslims who reject the extremism that leads to hate instead of hope," he said.

Obama started his speech by introducing himself as a "proud citizen of the United States and a fellow citizen of the world."

Police estimated that more than 200,000 people came to watch the speech, according to The Associated Press. Watch the crowds wait for Obama »

Shortly before the address began, Sen. John McCain, the presumptive Republican nominee, chided Obama and said he'd rather give a speech in Germany as president than as a presidential candidate.

"So we're going to be campaigning across the heartland of America and talking about the issues that are challenging America today," McCain said outside a German restaurant in Columbus, Ohio.

In a statement issued after the speech, McCain spokesman Tucker Bounds said, "Barack Obama offered eloquent praise for this country, but the contrast is clear."

"While Barack Obama took a premature victory lap today in the heart of Berlin, proclaiming himself a 'citizen of the world,' John McCain continued to make his case to the American citizens who will decide this election.

"John McCain has dedicated his life to serving, improving and protecting America. Barack Obama spent an afternoon talking about it," he said.

The Democrat said that his address was not a "political rally."

Crowds gathered at the Victory Column to listen to musical acts in the hours leading up to Obama's arrival.

Obama originally had hoped to speak in front of the iconic Brandenburg Gate, where President Kennedy was photographed during a 1963 visit after the rise of the Berlin Wall. Expressing solidarity with the people of the divided city during the same trip, Kennedy declared, "Ich bin ein Berliner."

That phrase, which means "I am a Berliner," expressed the unity of the West in the Cold War era.

The gate also was the site of a speech by President Reagan in 1987 in which he memorably urged Soviet leader Mikhail Gorbachev to "tear down" the wall.

But use of the landmark apparently was vetoed by German Chancellor Angela Merkel, who a spokesman Wednesday said disapproved of plans to co-opt it as a "campaign backdrop."

Asked whether he looked to Reagan's and Kennedy's Berlin speeches for inspiration, Obama said, "They were presidents. I am a citizen."

"But obviously, Berlin is representative of the extraordinary success of post-World War II effort to bring a continent together, to bring the West together -- East and West together," he said.

Nonetheless, as a youthful Democratic presidential hopeful who has promised change if elected and invoked comparisons with Kennedy, Obama's strategists hope a warm welcome from Germans will play well with voters.

Obama is in Germany for the latest leg of an international trip intended to bolster his foreign policy credentials at home and set out his vision for a new era of transatlantic cooperation.

His trip has taken him to Afghanistan, Iraq, Jordan, Kuwait, Israel and the Palestinian territories. Obama is expected to stop in France and Great Britain before returning to the United States.

Obama has said he is making the trip as a senator and not a presidential candidate.

Robin Oakley, CNN's European political editor, said Obama enjoyed widespread popularity in Europe.

"He is one of those politicians who reaches parts other politicians don't reach," Oakley said. "After the unpopularity of George W. Bush, the world is waiting to love America again, and many see in Obama, with his youth and his optimism, somebody who can bring that about."