According to reports the oldest victim of the killer was Sevda Dag, a 45-year-old Turkish woman.
Sonboly was found dead by police following a suspected suicide.
At a press conference Mrs Merkel said the events are "difficult to bear for everyone" and pledged to "find out the background" of what happened.
She added: "What lies behind the people of Munich is a night of horror - we are still shocked by the pictures and reports of the witnesses.
Victims: People leave the shopping mall after the mass shooting
AP Photo/Sebastian Widmann
"Nine people who were going shopping on the Friday evening, or wanted to eat something, they are now dead- hit and killed by the bullets of one single perpetrator.
"We are in deep and profound mourning for those who will never return to their families. The families, siblings, friends to whom everything will be void and empty today.
"I would like to tell them, in the name of many, many people in Germany, we share in your grief, we think of you and we are suffering with you.
"Our thoughts also go out to the numerous injured people - may they recover quickly and completely - they will receive all the support they need.
Shooting: The gunman lured people to McDonald's
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"Such an evening and such a night are difficult to bear for every one of us. They are even more difficult to bear because we have had so many different and difficult reports of horrors in the past few days."
Officials said the killer used a 9mm pistol and had 300 rounds of ammunition in his rucksack when he went on what they called a "classic shooting rampage".
There were indications the gunman had been in psychiatric care and treated for depression and articles about mass shootings were discovered when his flat was searched – but there is no link to Islamic State.
According to reports the killer had an "obvious" interest in Norwegian mass-murderer Anders Behring Breivik - who, five years to the day of the Munich attack, slaughtered 77 people.
