With the surge of social media, maliciously tampered public speeches, especially those from influential figures, have seriously affected social stability and public trust. Existing speech tampering detection methods remain insufficient: they either rely on external reference data or fail to be both sensitive to attacks and robust to benign operations, such as compression and resampling. To tackle these challenges, we introduce SpeechVerifer to proactively verify speech integrity using only the published speech itself, i.e., without requiring any external references. Inspired by audio fingerprinting and watermarking, SpeechVerifier can (i) effectively detect tampering attacks, (ii) be robust to benign operations and (iii) verify the integrity only based on published speeches. Briefly, SpeechVerifier utilizes multiscale feature extraction to capture speech features across different temporal resolutions. Then, it employs contrastive learning to generate fingerprints that can detect modifications at varying granularities. These fingerprints are designed to be robust to benign operations, but exhibit significant changes when malicious tampering occurs. To enable speech verification in a self-contained manner, the generated fingerprints are then embedded into the speech signal by segment-wise watermarking. Without external references, SpeechVerifier can retrieve the fingerprint from the published audio and check it with the embedded watermark to verify the integrity of the speech. Extensive experimental results demonstrate that the proposed SpeechVerifier is effective in detecting tampering attacks and robust to benign operations.