The club's chief executive David Allen will lead the search for a new manager, but will give Abbott an extended run to prove he deserves to be given the job on a full-time basis.
"It would be unfair to do it on a match-by-match basis. We have to give Greg a fair crack at it," he told the News & Star newspaper.
"We haven't agreed an exact timescale but we have got to be looking at until the January transfer window has been and gone to see who he brings in and who he moves out.
"Compared to other clubs, Carlisle United is on a stable financial footing, we've got money in the bank and Greg will be able to do things in the transfer window."