The theory of operator extensions in rigged Pontryagin spaces is used to develop two functional models for closed symmetric entire operators S with finite deficiency indices (p,p) acting in a separable Pontryagin space K. In the first functional model it is shown that every such operator S is unitarily equivalent to the multiplication operator in a de Branges-Pontryagin space B(E) of p×1 vector valued entire functions. The second functional model is used to parametrize a class of compressed resolvents of extensions S˜ of S in terms of the range of a linear fractional transformation that is associated with the model. This approach is independent of the methods used by Krein and Langer to parameterize a related class of extensions.