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I am reviewing a paper for a journal that has an open review policy. This means that when a paper is submitted to the journal, the paper is published online on the journal's website and when a decision is made, the reviews are published with the reviewers' names. If they want, reviewers can opt out and be anonymous.

I reviewed a paper where I was not anonymous. The decision was to request a major revision. I was invited to review a new version of the paper. I am still unsatisfied with some aspects of the paper but I do not think the problematic parts are sufficient to request a reject. However, I am reluctant to accept the paper with minor revision because I think the changes are substantial enough to require another round of review for checking the last version. If I could, I would propose another major revision, but the journal policy is that a major revision is either accepted (possibly with minor revision) or rejected.

So I thought I could contact the authors (whom I know) directly to tell them how to fix the issues, and then request a minor revision. Since they already know that I am a reviewer, this seems like it would not break any principles of good reviewing behaviour, would it?

Independantly of my precise case, and in order to make the answers useful to more people, it would be good to see opinions on what circumstances allow a reviewer to contact authors personally.

[BTW, I already asked the journal editors if this would be appropriate. At the time of writing the question, I'm waiting for their reply.]

Unless the editor gives you permission, I think it would be improper to deal with the authors directly. While it might speed things along a bit, it would also cut the editor and his/her staff out of the conversation.

It is better to just write your report to the editor and submit it in the usual way. This establishes a record of the revisions.

It also avoids a situation in which a reviewer would think that his/her comments were important enough to warrant co-authorship. That might not be your position, but some might want to consider it if the option were open.

Don't feel bad about the authors. The paper must eventually stand on its own, independent of any relationship between reviewers and authors. You are doing them a favor by being honest and having the editor in the loop aids that.

But the editor may have different views, in which case, you can follow them. You have done the right thing by asking.

I wouldn't do it. May be seen by the authors or the editors (or potentially other reviewers) as unfair pressure. Even if your meaning is innocent. Just file standard reviews with the editor and let it be at that.

Every year there are good and bad papers published and ones that are flawed but useful. Wash your hands of this and move on to other tasks of your own.

I see a conflict here. Your identity will be revealed after completion of review process and decision, and that too optional. Contacting directly the author means your identity will also be known to author before final decision. In this case they can possibly influence your decision directly or by a reference or sorry to say but possibly by mutual future settlement.
In my opinion it will raise questions over whole review process.