The 26-year-old star married Brand, 36, in a ceremony in India in October last year and recent reports claimed the pair were spending less and less time together and considering a trial separation.
However Perry later took to her Twitter page to put the rumours to rest.
She wrote: 'Just cause we don't flaunt our relationship doesn't mean there's something wrong w/it. Privacy is our luxury. #tabloidsrtrash #gossipisgross.'
Brand later supported his wife and wrote a message on his Twitter page as well.
He wrote: 'You tell em Mrs Brand! In Britain we're currently dismantling the scum media so I'm not tuned in to their brain-farting.'