Relieving letter govt job

I was working at an institute under a state govt ministry. It was a full time regular post, not yet permanent. I applied for a central govt job before I joined this state govt job and I cleared all exams and interviews of the central govt job while I was in the state govt job. I informed about my candidature and appearance at the qualifying exams through proper channel to my state govt office. I have resigned from this job mentioning that I cleared the central govt job and I mentioned my last working day after 3 weeks of my resignation application date. The institute is providing me no dues certificate but no relieving letter as the original state govt ministry will do so and they are delaying. If I wait for the state govt relieving letter, I may lose the central govt job. Can I join the central govt job by issuing my resignation letter, acknowledgement of the resignation and no dues certificate? My last date of joining is due in the next week. Please help.