Owning a dog in rented accommodation in Reykjavik??

Most of the rentals are privately owned, so it's up to the owners and sometimes the buildings if it is a larger apartment complex. Iceland was not very dog friendly for decades, so it isn't very common for people to have dogs as pets in the "city"

In conclusion, i recommend searching for places in smaller buildings rather than big blocks, and be prepared for a long search. It is probably wise to find the apartment first before getting the dog too.