Clarkson, who is hosting the show, said she was asked to hold a moment of silence for the 10 victims who died Friday, but chose instead to call for "a moment of action."
Police say the attacker had threatened officers with a hammer and refused to stop.
Justin Bieber, Miley Cyrus, Katy Perry, Robbie Williams, Take That, Liam Gallagher, and Little Mix were among those who hit the stage.
Organisers announced that the festival would resume after the "threat" proved to be unfounded.
German police said there were "concrete" indications of an attack on the Rock am Ring festival that draws thousands of people annually.
Ariana Grande will lead the "One Love Manchester" concert almost two weeks after her concert in the city was hit by a suicide bombing that killed 22 people and wounded 116. But there are concerns that survivors may miss out on free tickets.
Manchester bomber Salman Abedi grew up in neighbourhoods around south Manchester. Some in the area say poverty and under-funded social services are isolating young people and turning them against their communities.
British Prime Minister Theresa May hardens tone on Brexit talks as Britons prepare to elect a new government in ten days' time.
The latest arrest was of a 23-year-old man in Sussex. Britain has lowered its security level from "critical" to "severe," meaning the country remains on high alert a week after the suicide attack killed 22 at a concert in the northern English city.
The statement by British interior minister came as UK police released new photographs of the suspected bomber.
UK's top counter-terrorism officer Mark Rowley says police has arrested "key players" behind the Manchester bombing.
"They've covered the cobbles, but they'll never defeat all the dreamers and schemers who still teem through these streets," read Walsh in a heart-touching ode to the city.
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