Tens of thousands of people gathered in cities across Germany on Thursday to remember the victims of the attack.
On Wednesday, a 43-year-old German man, who has been identified as Tobias Rathjen, shot dead nine people of immigrant background in the Frankfurt suburb of Hanau before killing his mother and himself.
It was later revealed that Rathjen had left a manifesto espousing far-right, eugenicist and racist views.
Mr Seehofer also announced there would be an “increased presence” from police nationwide, particularly at mosques.
Germany’s president Frank-Walter Steinmeier addressed mourners at the main Hanau vigil and condemned the “brutal act of terror”.
“We stand together, we want to live together and we show that over and over again,” he said, as occasional shouts of “Nazis out” were heard from the crowd.
“That is the strongest way to fight hatred.”
The chant was heard again at an Eintracht Frankfurt football match on Thursday after several people interrupted a minute’s silence for the victims.
The attack came amid rising concerns about far-right extremism and the rise of the anti-migrant party Alternative for Germany (AfD), which is currently the third-largest party in the German parliament.
Lars Klingbeil, a top official in the centre-left Social Democratic Party, accused AfD on Friday of providing ideological material for extremists like the Hanau gunman.
“One person carried out the shooting in Hanau, that’s what it looks like, but there were many that supplied him with ammunition and AfD definitely belongs to them,” Mr Klingbeil told public broadcaster ARD.
AfD has rejected all responsibility for far-right attacks, such as an antisemitic attack on a synagogue and the killing of a regional politician last year.
Joerg Meuthen, the far-right party’s co-leader, has chosen to not define the attack as far-right extremism and criticised people who have made political points about the incident.
“This is neither right nor left terror, this is the delusional act of a madman,” Mr Meuthen wrote on Twitter.
“Any form of political instrumentalisation of this terrible act is a cynical mistake.
“Instead, all the people of our country should mourn the victims together with their relatives.”
Additional reporting by AP