"According to what we know so far, especially based on statements made by the accused to the police, he has been planning to kill Jews for several weeks," Berlin police said on Saturday.
The incident had "connections with the Middle East conflict", the public prosecutor's office added.
The knife attack on Friday left a 30-year-old Spanish tourist hospitalised with wounds to his throat.
Authorities say the suspect, who was apprehended by police hours after the incident, is a 19-year-old Syrian refugee who came to Germany as a minor in 2023.
The arrest warrant has been issued against the attacker for grievous bodily harm and attempted murder. The man is now in custody.
Police at the scene on Friday noticed the suspect's blood-smeared hands and trousers. He reportedly approached policemen who then apprehended him.
He is believed to have specifically targeted the Holocaust Memorial in the German capital, which commemorates the approximately six million Jews murdered under Nazi rule.
The suspect was also said to be carrying a Koran and a prayer rug in his rucksack, suggesting a religious motive for the attack.
"Whether there is a mental illness is the subject of the investigation," said police.
Authorities in the eastern state of Saxony, where the suspect lived, said he was known to police for earlier criminal offences.
The incident on Friday came just two days before Germany heads to the polls after an election campaign dominated by a series of attacks attributed to foreign nationals.
Interior Minister Faeser expressed her horror at attack, calling for the alleged perpetrator to be punished severely and "deported directly from prison".
"The knife attack at the Berlin Holocaust Memorial is a heinous and brutal crime," said Faeser in a statement on Saturday.
"Anyone who commits such offences and abuses protection in Germany in the most disgusting way has forfeited any right to be in our country," said Faeser.
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