A 26-year-old suspect, a French national arrested after the attack on Saturday, had pledged allegiance to Islamic State in a video recorded beforehand, anti-terrorism Prosecutor Jean-Francois Ricard said on Sunday.
The suspect had told police he was angry about the situation in Gaza and the fact that "so many Muslims are dying in Afghanistan and in Palestine," Interior Minister Gerald Darmanin said.
The German tourist suffered fatal injuries when he was attacked on the Quai de Grenelle, a few feet from the Eiffel Tower, authorities said.
The attacker was chased by police and assaulted two other people, including the British man, with a hammer, officials added.
European security officials have warned of a growing risk of attacks by Islamist militants amid the Israel-Hamas war, with the biggest threat likely from "lone wolf" assailants who are hard to track.
An investigation was under way into murder and attempted murder in connection with a terrorist organisation, prosecutor Ricard told a news conference. Three other people from the suspect's family or entourage were in police custody, he added.
The suspect had in 2016 been sentenced to four years in prison for planning another attack, and had been on the French security services' watch list, Darmanin said. He was also known for having psychiatric disorders, Darmanin added.
German Chancellor Olaf Scholz said on X that he was "shocked" by the attack. Britain's foreign ministry said it was working with French authorities to support the British man.
France has been on high alert since raising its security threshold in October, when a Chechen-origin man with a knife killed a teacher in a school in northern France.
The attack in central Paris comes less than eight months before the French capital is due to host the Olympic Games and could raise questions about security at the global sporting event.
The city was planning an opening ceremony on the Seine river with the potential to attract as many as 600,000 spectators.
Paris police chief Laurent Nunez told BFM TV on Sunday the terrorism threat was "permanent" and that the opening ceremony had been prepared with security measures taking into account a "high level" of terrorism threat.
"I send all my condolences to the family and loved ones of the German national who died ... during the terrorist attack in Paris and think with emotion of the people currently injured and in care," President Macron said on the social network platform X.
Prime Minister Elisabeth Borne wrote on X: "We will not give in to terrorism."
