The Abstractness and modality of interpersonal communication have a considerable impact on comprehension. They are relevant for determining thoughts and constituting internal models of the environment. Whereas concrete object-related information can be represented in mind irrespective of language, abstract concepts require a representation in speech. Consequently, modality-independent processing of abstract information can be expected. Here we investigated the neural correlates of abstractness (abstract vs. concrete) and modality (speech vs. gestures), to identify an abstractness-specific supramodal neural network. During fMRI data acquisition 20 participants were presented with videos of an actor either speaking sentences with an abstract-social [AS] or concrete-object-related content [CS], or performing meaningful abstract-social emblematic [AG] or concrete-object-related tool-use gestures [CG]. Gestures were accompanied by a foreign language to increase the comparability between conditions and to frame the communication context of the gesture videos. Participants performed a content judgment task referring to the person vs. object-relatedness of the utterances. The behavioral data suggest a comparable comprehension of contents communicated by speech or gesture. Furthermore, we found common neural processing for abstract information independent of modality (AS >CS boolean AND AG >CG) in a left hemispheric network including the left inferior frontal gyrus (IFG), temporal pole, and medial frontal cortex. Modality specific activations were found in bilateral occipital, parietal, and temporal as well as right in ferior frontal brain regions for gesture (G >S) and in left anterior temporal regions and the left angular gyrus for the processing of speech semantics (S >G). These data support the idea that abstract concepts are represented in a supramodal manner. Consequently, gestures referring to abstract concepts are processed in a predominantly left hemispheric language related neural network.