"assure" means promise or guarantee "ensure" means "make certain" or "make sure" So the correct sentence is "I assure you" = "I promise you" "I ensure you" would make no sense. An example using "ensure" is "I ensured he went to school" = "I made certain/sure he went to school"

"I can ensure to you Madam that you will be perfectly safe walking over this bridge, you have my assurance on that, it passed the safety checks only last week. The bridge is as safe as a (joke her very religious)" However nobody can actually assure or ensure anybody of anything, that is for the grammarians and linguist to debate over. If you want to comfort and to reassure it is assure if you are confirming that something will not happen it is ensure. But ensure is normally used in the sense of giving demands or official notices etc or seeking reassurance yourself or given advice yourself. "Please take care and ensure you do not let the children walk too close to the cliff edge" ."you will be careful and ensure you do not get into any trouble won't you ?" "Contractors must ensure that they lock the gates on leaving the storage facility" We use ensure generally speaking in this manner, and assure to give comfort and reassurance.

"I assure you" is correct "assure" means "tell someone something positively to dispel any doubts" whereas "ensure" means "make certain that (something) will occur or be the case" Example "I can assure you it will not rain tomorrow, so do not take an umbrella"

The other answers are all good, but here's a short version: you "ensure" something, but you "assure" someone (about something). "I can ensure that the work will be done on time." "I can assure YOU that the work will be done on time." "I told him that I could ensure our success." "I assured HIM that we would succeed."

it helps, Kristen, much obliged:)