To coordinate cell fate with changes in spatial organization, stem cells (SCs) require specific and adaptable systems of signal exchange and cell-to-cell communication. Pluripotent embryonic stem cells (ESCs) use cytonemes to pair with trophoblast stem cells (TSCs) and form synthetic embryonic structures in a Wnt-dependent manner. How these interactions vary with pluripotency states remains elusive. Here we show that ESC transition to an early primed ESC (pESC) state reduces their pairing with TSCs and impairs synthetic embryogenesis. pESCs can activate the Wnt/β-catenin pathway in response to soluble Wnt ligands, but their cytonemes form unspecific and unstable interactions with localized Wnt sources. This is due to an impaired crosstalk between Wnt and glutamate receptor activity and reduced generation of Ca2+ transients on the cytonemes upon Wnt source contact. Induced iGluR activation can partially restore cytoneme function in pESCs, while transient overexpression of E-cadherin improves pESC-TSC pairing. Our results illustrate how changes in pluripotency state alter the mechanisms SCs use to self-organize.