This paper proposes a novel approach to combinatorial test generation, which achieves an increase of not only the number of new combinations but also the {\em distance} between test cases. We applied our distance-integrated approach to a state-of-the-art greedy algorithm for traditional combinatorial test generation by using two distance metrics, Hamming distance, and a modified chi-square distance. Experimental results using numerous benchmark models show that combinatorial test suites generated by our approach using both distance metrics can improve interaction coverage for higher interaction strengths with low computational overhead.