Many systems have been built to employ the delta-based iterative execution model to support iterative algorithms on distributed platforms by exploiting the sparse computational dependencies between data items of these iterative algorithms in a synchronous or asynchronous approach. However, for large-scale iterative algorithms, existing synchronous solutions suffer from slow convergence speed and load imbalance, because of the strict barrier between iterations; while existing asynchronous approaches induce excessive redundant communication and computation cost as a result of being barrier-free. In view of the performance trade-off between these two approaches, this paper designs an efficient execution manager, called Aiter-R, which can be integrated into existing delta-based iterative processing systems to efficiently support the execution of delta-based iterative algorithms, by using our proposed group-based iterative execution approach. It can efficiently and correctly explore the middle ground of the two extremes. A heuristic scheduling algorithm is further proposed to allow an iterative algorithm to adaptively choose its trade-off point so as to achieve the maximum efficiency. Experimental results show that Aiter-R strikes a good balance between the synchronous and asynchronous policies and outperforms state-of-the-art solutions. It reduces the execution time by up to 54.1% and 84.6% in comparison with existing asynchronous and the synchronous models, respectively.