The variety of cloud services (CSs) that are described, their non-uniform naming conventions, and their heterogeneous types and features make cloud service discovery a difficult problem. Therefore, an intelligent cloud service discovery framework (CSDF) is needed for discovering the appropriate services that meet the user's requirements. This study proposes a CSDF for extracting cloud service attributes (CSAs) based on classification, ontology, and agents. Multiple-phase classification with topic modeling has been implemented using different machine learning techniques to increase the efficiency of CSA extraction. CSAs that are represented in different formats have been extracted and represented in a comprehensive ontology to enhance the efficiency and effectiveness of the framework. The experimental results showed that the multiple-phase classification methods with topic modeling for CSs using a support vector machine (SVM) obtained a high accuracy (87.90%) compared to other methods. In addition, the results of extracting CSAs showed high values for precision, recall, and f-measure of 99.24%, 99.24%, and 99.24%, respectively, for Java script object notation(JSON) format, followed by 99.05%, 97.20%, and 98.11% for table formats, and with lower accuracy for text format (90.63%, 86.57%, and 88.55%).