The group, fronted by Brandon Flowers, reunited to play at the Hard Rock Calling event but have recently been working on their own projects.
Drummer Ronnie Vannucci says they support each other whether they are apart or together.
He told UK newspaper the Daily Star: 'I feel like they support me and I feel like I support them. There's no rivalry. I'd never even thought of it like that. It'd be cool if there was, though.'
Vannucci, 35, has also set up his own record label.
He said: 'I started a label but I don't know what I'm doing with that yet. Right now it's more of a function of putting my record out. Maybe I'll invest in a second solo album, or I'll give the money away to my family.'