DONETSK, Ukraine — For Larisa Horlova, a cashier, making the trip from rebel-held territory to Ukraine proper had been a routine matter, despite the shells that sometimes pounded into fields near the road as she drove. She did it every week or so to get money from her Ukrainian bank account, since A.T.M.s are no longer functioning in Donetsk.

But on Wednesday, when she made the often perilous dash over pavement slicked by melting snow to a Ukrainian border outpost, she found not safety but an order to turn around and drive back.

“They say I should live on the Ukrainian side, but I cannot travel back and forth,” Ms. Horlova said, standing on the shoulder of the road, amid a crowd of other bewildered residents.

Indeed, with a new offensive in full swing, the Ukrainian authorities are now doing all they can to halt cross-border movement, deploying the full force of a Byzantine bureaucracy on the more than three million people living in rebel-held areas.