Frequently interrupted by robust applause, Merkel reiterated her country's commitment to fostering security in Afghanistan and also said that a nuclear bomb in the hands of Iran "is not acceptable."
In the first address by a German chancellor to Congress since Konrad Adenauer in 1957, Merkel put special emphasis on the need for a global agreement on climate change - one she said she hoped could be forged at an international conference next month in Copenhagen.
"We have no time to lose," she declared. Merkel said she recognized that no deal could be successful without the support of China and India - but that if a deal were struck, she said she was sure those two fast-growing economies could be persuaded to sign on.
"Today's generation needs to prove that it is able to meet the challenges of the 21st century, and that, in a sense, we are able to tear down walls of today," she said.
Merkel cited as clear proof of global warming icebergs that are melting in the Arctic, African people forced to flee their homelands because of drought and the rise in global sea levels.
The chancellor met at the White House with President Barack Obama before her speech to the joint session of Congress; Obama shares her support for a strong international agreement on global warming, although considerable skepticism lingers in Congress.
And, whereas at other times in her speech she received full standing ovations, when she mentioned the climate change deal only part of her audience rose to applaud. Many Republican lawmakers remained seated.
After their White House meeting, Obama said, "The United States, Germany and countries around the world, I think, are all beginning to recognize why it is so important that we work in common in order to stem the potential catastrophe that can result if we continue to see global warming continue unabated."
He also said he appreciated "the sacrifices of German soldiers in Afghanistan."
Merkel used the Oval Office session and her speech to Congress to express gratitude for American support throughout the process leading up to German reunification.
She praised both the U.S. pilots who ran dangerous missions shortly after World War II to airlift food and supplies to West Berlin and to the millions of American troops and diplomats stationed in Germany between the end of the war and today.
Without their help, she said, "overcoming the division of Europe would simply not have been possible."
On Iran's nuclear program, Merkel said that allowing Iran to have nuclear weapons, especially with a leader that denies the Holocaust, is "nonnegotiable."
"A nuclear bomb in the hands of an Iranian president who denies the Holocaust, threatens Israel and denies Israel the right to exist is not acceptable," she said.
The Obama administration has called on Germany to agree to stiffer economic sanctions against Iran if Tehran does not permit international restrictions on its nuclear activities.
Merkel said Germany agreed that it was important "to meet this threat head on ... if necessary, through tough economic sanctions."
On the subject of Afghanistan, Merkel said Germany will "travel this road together, every step of the way" with the United States. While Washington has indicated it would like to see Germany and other partners in Afghanistan increase their forces, the war is highly unpopular in Germany.
She acknowledged that the U.S. and Germany don't see eye to eye on all issues. But she cited a "common basis of shared values."
As leader of Europe's largest economy, Merkel pledged to keep working with the United States and other Group of 20 major economies to take coordinated steps to prevent a global financial meltdown like the recent one.
"We have to do everything to prevent such a crisis in the future," she said.
Monday marks 20 years since the Berlin Wall was pulled down, leading to the reunification of Germany. The German capital had been divided among the victorious European allies at the end of World War II and quickly became a symbol of the Cold War.
Merkel's visit to Washington comes a week after she was sworn in for a second term. Her formation of a new center-right coalition has created some expectations in Washington that the coalition would make it easier for Merkel to support the United States on Afghanistan and other foreign policy issues, including reining in Iran's nuclear program.
Annette Heuser, executive director of the Bertelsmann Foundation Washington, a nonprofit organization that focuses on trans-Atlantic cooperation, said political pressures in Germany against the war in Afghanistan remain the same for Merkel.
"On Afghanistan, it will be a big challenge for her to balance the speech for both an American and a German audience," Heuser said.
Even as Merkel was making a case for urgent action on global warming, a GOP boycott forced a delay of votes in a Senate committee on a bill to curb greenhouse gas emissions. The Republicans protested that more study was needed on the bill's costs.
And in Barcelona, Spain, African countries briefly boycotted U.N. climate talks on Tuesday, claiming industrial countries had set carbon-cutting targets too low. They later said they were ending the protest after winning promises for more in-depth talks on emission levels.
Delegates to the Barcelona talks are preparing for next month's major meeting in Copenhagen.
Associated Press writers H. Josef Hebert in Washington and Arthur Max in Barcelona contributed to this report.