I'd be inclined to differ from M56 on this one. 'Rest' here means 'remain'; and 'assured' is an adjective, meaning <satisfied as to the certainty or truth of a matter>(Merriam-Webster).
So I'm not sure how you could use 'rest assure'; though I note that it has a strong Internet presence as a typo.
These are characteristic examples of 'rest assured':
1. You can rest assured that the cheque's in the post.
2. Rest assured that we'll do everything in our power to apprehend the perpetrators.
3. You may rest assured that my intentions are entirely honourable.
MrP