I have received an oral offer from University A, but a few days later I got the interview invitation from University B and I attended it. I am still waiting for the interview result which could come up until next week or the week after next. Now University A asked me whether I will accept the offer, so they can start the administration application. I would like to request a longer decision time or defer this offer so that I can wait for the decision from University B. How do I write this email? Can I just tell University A the truth that I'm applying for an another position?
The position in University B suits my career plan much better than A, and pays much more. This is why I really want to do something for this position. Can you please advise me on how to write this email?
Edit: I am applying for funded PhD position in Europe. The first offer from University A came in 2nd May. I decided to accept this offer (and I thought a "yes" during the interview means an acceptation of the offer) and started to apply for a necessary certificate which is required to study in the specific country. The interview invitation of University B came in 11th May. I interviewed in 17th May and the interviewer told me they will inform me of the result 3 to 4 weeks after (which is around the first half of June). These days I confirmed some details with University A and keep in touch with University B. 31st May I received an email from University A, asking whether I will accept the offer.