The private gathering on the eve of the anniversary of the atrocity comes against the backdrop of angry recriminations by many of the bereaved, who say official incompetence and neglect since the assault have inflicted fresh pain.
Merkel acknowledged Monday that "some had wanted such a meeting earlier" but pledged to listen the families' concerns.
"It is clear to me that their suffering, this complete transformation of their lives, cannot be put right," she told reporters ahead of the gathering.
Last December 19 at 8:02 pm, Anis Amri, a 24-year-old Tunisian who had failed to obtain asylum, rammed a stolen truck into crowds at the market on the Breitscheidplatz, a popular destination for Berliners and tourists alike.
The victims came from Germany as well as countries including Israel, Italy, the Czech Republic and Ukraine.
The Islamic State group claimed responsibility the next day, and Amri was shot and killed four days later by police in Italy, where he had previously lived.
More than 70 people were injured in the attack, the deadliest ever carried out by IS in Germany.
"Almost a year after the attack, we note that you have not shared your condolences with us either in person or in writing," the letter said.
"In our opinion, this means that you are not living up to the responsibilities of your office."
A government-commissioned report released last week identified a litany of shortcomings in the response to the tragedy.
Some relatives desperately searching for their loved ones were told only three days after the attack that a family member had perished, even though they could have been given early warning through facial identification.
"Such experiences should never be repeated," he said, adding that Germany "was not prepared" to deal with the attack's aftermath.
The government has paid out 1.6 million euros (USD 1.9 million) in compensation to the wounded and victims' families.
Another factor keeping the wounds raw has been revelations in the media about administrative gaffes and missteps leading up to the attack.
Amri, who arrived in Germany in the summer of 2015, at the height of the refugee influx, registered under several different identities.
But Amri was never deported or arrested.
Merkel noted Monday that a parliamentary inquiry had been called to "get to the bottom of all the questions surrounding the perpetrator".
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