Chances of getting a postdoc with low number of papers I'm a Ph.D. graduate in biotechnology/molecular biology, who is actively seeking a post-doctoral position at a US or Europe-based institute. I'm neither from US, nor from Europe. Thus, I believe, my chances of getting a postdoc position is slightly harder, compared to some others.

My Ph.D. supervisor was very strict in allowing Ph.D. students graduate, only after at least 3 different projects have been completed. My first project was completed long time ago and its paper was published at a high-impact journal. However, my second paper was rejected by an editor, thus we recently divided it into 2 sections and submitted them to average-impact journals. They are under review right now.

The 3rd project's paper will be submitted in 2 weeks.

I've contacted many well-known professors in my field, and they do respond to my e-mail, mostly saying they are interested in accepting me in their group, only if I can secure my own funding. Or, they say they are waiting for a grant to come up.

But, every e-mail I get from them sounds very familiar to each other. They either have no new grant, or would like me to have my own funding.

A PI I know recently told me, my chances were extremely low if I did't have at least 4 published papers. I've got 1 published, but 2 "under review" articles, and I'm the first-author of all.

Do you agree with this PI? Should I wait until I get to reach to the level of having 4 published papers, which might happen after 6 months or something. Or, do you think papers "under review" are nearly as impactful as papers "published"?
In the UK and Scandinavia at least, provided you show that those papers are in review you should be ok except for very highly competitive labs. The 'well-known professors' are most likely to be running those kinds of labs BUT you may well still get in if you are experienced in a topic or technique they are looking for. 

I honestly doubt the professors are lying or trying to brush you off; nearly all postdoc positions only come up when project funding comes through. Bear in mind that the professors are probably answering several such emails a week so they do indeed keep a 'stock' reply and that is fair enough. 

So don't wait for your publications to happen but look for advertised positions in your specialism and/or with your skillset named. Good websites are jobs.ac.uk and Euraxess. 

Side note: I am aware that candidates from not-USA-or-Europe often get a harder time which is regrettable. My answer stands but I wanted to acknowledge that you do have it tough.