The actress, 31, and tech magnate, 46, were spotted out and about in Australia just days after news of their split broke — and now they’re clearing the air on their breakup.
In a joint statement, the pair told PEOPLE exclusively: “Having read recent articles about our relationship, we would like to speak for ourselves. The distance has been really tough on our relationship, because we haven’t been able to see each other much. All relationships have their ups and downs, of course.
“People occasionally send out speculation, which has no basis in fact, without our knowledge, believing that that they have our best interests in mind. Sometimes, other agendas are at work. It can get a little weird… However, we would like to state directly that we have the utmost respect for one another, and it would be troubling if anyone had the impression that we thought otherwise.
“As a closing note, it is worth bearing in mind that events are always amplified and dramatized in a high profile relationship, whether the people involved like it or not (and we definitely don’t). The reality is that this is just a normal relationship with a giant magnifying glass applied.”
As PEOPLE reported Monday, Musk and Heard — who had spent time with the Tesla founder’s five sons — called it quits because of increasingly busy schedules.
“They had fun for a few months, but are both very busy with work now. It was getting hard to find time to see each other,” a source told PEOPLE at the time.
On Tuesday, Heard addressed the split on Instagram, writing that she and Musk “care deeply for one another and remain close.”
The pair were first linked together last year, as each was weathering a public uncoupling: Heard and actor Johnny Depp finalized their divorce in January, while Musk filed for divorce from Westworld actress Talulah Riley in early 2015.