Embryonic stem cells (ESCs) can contribute to the tissues of chimeric animals, including the germline. By contrast, epiblast stem cells (EpiSCs) barely contribute to chimeras. These two types of cells are established and maintained under different culture conditions. Here, we show that a modified EpiSC culture condition containing the GSK3 inhibitor CHIR99021 can support a germline-competent pluripotent state that is intermediate between ESCs and EpiSCs. When ESCs were cultured under a modified condition containing bFGF, Activin A, and CHIR99021, they converted to intermediate pluripotent stem cells (INTPSCs). These INTPSCs were able to form teratomas in vivo and contribute to chimeras by blastocyst injection. We also induced formation of INTPSCs (iINTPSCs) from mouse embryonic fibroblasts by exogenous expression of four reprogramming factors, Oct3/4, Sox2, Klf4, and c-Myc, under the INTPSC culture condition. These iINTPSCs contributed efficiently to chimeras, including the germline, by blastocyst injection. The INTPSCs exhibited several characteristic properties of both ESCs and EpiSCs. Our results suggest that the modified EpiSC culture condition can support growth of cells that meet the most stringent criteria for pluripotency, and that germline-competent pluripotency may depend on the activation state of Wnt signaling.