CE Marking IVDs produced under ISO 9001

Is it permitted to self mark IVDs that are produced under an ISO 9001 or is production under ISO 13485 mandatory?

My interpretation is as follows:
1) The IVD-directive of 27 October 1998, does not contain any reference to ISO 13485. The IVD-directive only expresses the requirement of having a quality management system, NOT what standard is to be used for the QMS.
2) As long as the elements of vigilance, traceability and design are added to and guarded by the 9001 QMS, a QMS under ISO 9001 is accepted for the production of IVDs.
3) Based on points 1 and 2, an IVD produced under ISO 9001 can be CE self marked.

I am very interested to know if this approach is correct. Please motivate any disagreement you have with it since that is important information for me.

Thank you in advance for your assistance.

Re: CE marking IVDs with produced under ISO 9001?

It's true that the IVDD doesn't contain a reference to ISO 13485, but it does contain requirements for a QMS more than just "have a QMS." It's also true that it's not a requirement to comply with EN ISO 13485, as it's a harmonized standard, but your QMS must comply with the regulatory requirements. So if you don't want to use EN ISO 13485, you may want to do a gap analysis between what the IVDD requires to be in your QMS and what the ISO 9001 QMS contains, and that would tell you if it's possible to self-certify an IVD with an ISO 9001 QMS, or even with the extra elements you named (I don't remember the specific requirements off the top of my head).