By Paul Carrel

BERLIN (Reuters) - Chancellor Angela Merkel defended democratic values and multilateral cooperation on Wednesday, in her first major speech since announcing she will seek a fourth term, but insisted Germany "can't solve all problems" in the world.

Merkel evoked the experience of Germany's post-war division to stress that democracy and freedom cannot be taken for granted, saying Europe should work with the United States and other allies to defend those values.

With the imminent departure of U.S. President Barack Obama, Merkel, 62 years old and already in power for 11 years, is left as the senior leader anchoring a Western alliance shaken by Donald Trump's U.S. election victory.

"I am deeply convinced that openness will bring us more security than isolation," she told the Bundestag lower house of parliament in a 40-minute speech on her government's priorities.

In an increasingly complex world destabilized by terrorism, Merkel said people and countries around the globe faced a choice between turning in on themselves or defending the values of democracy and engaging with international partners.

Without naming him, she appealed to Trump to work together.

Rejecting isolationism, she made a plea to "defend our values, which we consider right and important, not just at home but by trying to support them with our European partners, with the United States, with allies around the world."

Trump, who takes office on Jan. 20, made attacks on international trade deals a cornerstone of his election campaign, during which he also slammed members of the NATO alliance for not paying enough for their own defense.

Merkel, who on Sunday rejected the responsibility that was pushed onto her after Trump's win as "grotesque and absurd", clearly circumscribed the limits of Germany's international leadership.

"We cannot tackle all the world's hunger, nor can we solve the problems of 65 million refugees, nor can we change the political order everywhere the way we would like it," she said.

But, as Germany prepares to take over the G20 presidency next month, the conservative chancellor said Berlin should engage with other countries to make a success of globalisation.

"I say that we should work with others to frame globalisation on the basis of common ground and multilateralism," she said.

Merkel opened her speech by quoting Nobel prize winner Mario Vargas Llosa as saying in 2014 that the readiness to live together with people who are different was one of the biggest steps for people on the way to civilization.

"This statement moved me, because it comes back to what we are made of," she said. "A little more than quarter of a century after the fall of the (Berlin) Wall and German reunification ... people are realizing that what we have taken as given is no longer a given."

(Additional reporting by Madeline Chambers; Editing by Dominic Evans)