"There are additional indications which support this," he said. "This is why it's so important that the manhunt is successful."
A massive search is underway for Amri, 24, who is considered violent and believed to be armed.
A European arrest warrant was issued for Amri, and authorities offered a reward of up to 100,000 euros (about $104,000) for information on his whereabouts.
Elaborating about the investigation hours after de Maiziere spoke, a spokeswoman for the federal prosecutor's office said authorities also found fingerprints "outside of the door of the truck, and inside."
"Our investigation makes us assume that Anis Amri did drive the truck," the spokeswoman, Frauke Koehler, told reporters Thursday evening.
German police carried out raids in cities across the country Thursday, including at a refugee shelter in Emmerich, in North Rhine-Westphalia, where Amri is believed to have stayed.
Meanwhile, newly released dashcam footage showed the truck speeding through an intersection towards the Christmas market, seconds before it crashed into the crowd.
The video is the first released so far showing the truck at the moment of impact.
According to German investigative files obtained by CNN on Thursday, Amri had ties to an ISIS recruitment network in Germany and had previously discussed launching an attack there.
Amri and several members of the so-called Abu Walaa network backpacked more than 10 miles in Germany to get into shape as they prepared to travel to join ISIS, a police informant inside the network told investigators, according to investigative files obtained by CNN.
That December 23, 2015, training session and others were led by Boban Simeonovic, a leading German-Serbian figure in the network, according to the informant.
In late 2015 and early 2016, Simeonovic personally tried through his contacts at a mosque in the northern German town of Hildesheim to arrange logistics for Amri to leave the country, according to the files.
Amri communicated with the radical circle in Germany using the encryption app Telegram, a police informant inside the group told investigators, according to the investigative file obtained by CNN.
4 arrested in November
The main figure in the network, Ahmad Abdulaziz Abdullah -- a 32-year-old Iraqi national also known as Abu Walaa -- and four others were arrested and charged with terrorism offenses in November.
Ralf Jaeger, interior minister of the German state of North Rhine-Westphalia, said Wednesday that he could not confirm a link to Abu Walaa.
Amri was particularly close to Simeonovic, who was also charged in December, a German intelligence official told CNN.
Amri is mentioned several times by name in the 345-page investigative file, which underpinned the case built by prosecutors.
"Anis spoke several times about committing attacks," a police informant told German investigators, according to the files. The informant said Simeonovic and another member of the network "were in favor of that and gave him a place to hide."
Members of the Abu Walaa network also discussed driving a truck full of gasoline with a bomb into a crowd, the police informant told investigators, according to the documents.
Amri is thought to have been in Germany since July 2015, having traveled there from Italy, where he'd served time in prison for arson at a refugee center in Lampedusa.
'We are a target'
Speaking alongside de Maiziere, German Chancellor Angela Merkel admitted that Germany has "known for a long time ... that we are a target for Islamist terrorists."
German authorities are working at full speed to find the suspect, she said, alongside other countries that "are very much familiar with the challenges of terrorist attacks."
Merkel also had words of support for the victims and their families. "I am confident that during this test we are going through, we will persevere," she added.
The Breitscheidplatz Christmas market reopened Thursday after police said they had completed their investigation at the attack scene.
Candles and flowers have been left at makeshift shrines remembering the victims. People walked by quietly, some wiping tears from their eyes, and a couple of musicians sang "We Have no Fear." Vendors stood quietly as people passed their stalls.
Pressure on Merkel
The emerging details may increase the political pressure on Merkel over her government's generous acceptance of refugees.
Germany took in more than 890,000 asylum seekers last year, a much higher number than other European nations.
The issue contributed to defeats for Merkel's Christian Democratic Union in Berlin and her home state of Mecklenburg-Vorpommern during regional elections this year.