Merkel, who interrupted a summer holiday to face the media in Berlin, said the four assaults within a week were "shocking, oppressive and depressing" but not a sign that authorities had lost control.
The German leader said the assailants "wanted to undermine our sense of community, our openness and our willingness to help people in need".
"We firmly reject this," she said at a wide-ranging news conference.
Merkel repeated her rallying cry from last year when she opened the borders to people fleeing war and persecution, many from Syria, which brought nearly 1.1 million migrants and refugees to the country in 2015.
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"We have already achieved very, very much in the last 11 months."
Merkel was speaking after a axe rampage, a shooting spree, a knife attack and a suicide bombing stunned Germany, leaving 13 dead, including three assailants, and dozens wounded.
Three of the four attackers were asylum seekers, and two of the assaults were claimed by the Islamic State group.
Merkel said that she would not allow jihadists, following a series of deadly attacks in France, Belgium, Turkey and the US state of Florida as well as Germany, to keep her government from being guided by reason and compassion.
"It is my deep conviction that we cannot let our way of life be destroyed."
While the German political class has largely called for calm, opposition parties and rebels from Merkel's own conservative bloc have accused her of exposing the country to unacceptable risks without stricter controls on people let in.
"Islamist terrorism has unfortunately arrived in Bavaria," the state's interior minister Joachim Herrmann told reporters today, renewing calls by his Christian Social Union party for an upper limit on the number of new asylum seekers.
The deadliest attack came on Friday when a German-Iranian teenager who was born and raised in Munich opened fire at a downtown shopping mall, killing nine people before turning the gun on himself.