[sosilkj]

I agree with the above post. The rejection and subsequent reaching out should be viewed by you as though the conversation/process continued unabated.

I'll make an additional comment. From your description, it does not appear that either company has made you an offer yet. At this stage in the game, you don't really have much leverage. Job offers in hand are leverage. Your strategy should be to continue forward in parellel with as many companies as you can. Snagging a job offer from one is the best way to improve you chances with all the others. Having two offers (or more) gives you much, much better chance of optimizing your situation -- when companies are aware that their offer is not the only one on the table, they have more incentive to work to sweeten the package for you. All this to say: the idea of 'buying time' is totally the wrong way to be thinking about this; it pushes things in the wrong direction timeline-wise, since you want to moving things forward on all fronts to secure those job offers. There's no time to buy until you have at least one job offer.