The attacks brought the German chancellor fresh criticism for her decision last year to welcome refugees. More than one million asylum seekers were registered in Germany in 2015, although the influx has since slowed dramatically.
Mrs Merkel said at a news conference that Germany will “stick to our principles” and give shelter to those who deserve it.
“We will manage this,” she said, repeating a mantra she coined last August.
She called for a better “early warning system” against signs of radicalisation, faster progress on plans to create a centre to help crack encrypted messages and better international intelligence cooperation, among other measures.
But she said it was too early to say what more may be required beyond the tightening of asylum and security laws undertaken in recent months.
“Wherever there are gaps, we will have to act – just as we have so far – so that it is clear that we are doing everything humanly possible to ensure security in our free, democratic state of law,” Ms Merkel said.
Two of the attacks – an axe rampage near Wuerzburg that wounded five and a suicide bombing that injured 15 outside a bar in Ansbach – were the first in Germany to be claimed by the Islamic State group. Both of the attackers, asylum seekers who arrived over the past two years, were killed.
“We will do everything to clear up the barbaric acts, find the people behind them and punish them, and then we will have to decide where further measures are necessary,” Mrs Merkel said. She added that Germany owes that to the victims, their relatives, its own security and also “to all the many innocent refugees”.
“That two men who came to us as refugees are responsible for the acts in Wuerzburg and Ansbach mocks the country that took them in,” Mrs Merkel said. “It mocks the helpers who took so much care of the refugees and it mocks the many other refugees who really seek help against violence and war.”
The chancellor has faced criticism from opponents for her muted response to the four attacks.
Mrs Merkel dismissed that, and rejected the notion that she might feel guilt about the attacks. “I have the feeling that I am acting responsibly and correctly, and no other feelings,” she said.