The two were among a group of tourists who stripped off their clothes at Mount Kinabalu on May 30.
A week later, an earthquake in the area killed 18 people. Some local people said the foreigners had offended the mountain spirits and were to blame.
The Petersens were among four people who were arrested and fined $1,800 each.
On Tuesday, the siblings posted a statement on their private Facebook pages. Both issued the same statement.
Here is what Danielle said:
"Lindsey and I wish to express that we are deeply sorry for offending the local indigenous people of the Mount Kinabalu region. During our personal trekking experience, we were not made aware of the sacredness of the mountain. The contents of our hearts and everything else that was laid bare during our summit experience, were a reflection of the exuberance and joy we felt for our achievement of climbing the tallest peak in South East Asia; there was absolutely no ill intent.
'The 'Dynamic Duo' also wish to express gratitude to everyone who supported us in every way during this ordeal; to our security, a quick trial and a safe return home. This is an experience that we have learned from and will never forget."
The post ended with a quote attributed to Mark Twain:
"Clothes make the man. Naked people have little or no influence in society."