Yes. There is even an active function that allows you sign arbitrary bits to check if the passport actually contains the private key. Otherwise you could spoof a passport by just replaying the government signed data.
Source: I have been working on a blockchain implementation in the past that was compatible with the cryptographic functions in an NFC passport. Basically using a standard NFC passport as a cold wallet.
Fun fact. The cryptographic system even differs per country.
E.g. the Dutch don't trust the NIST elliptic curves so use the brainpool curves instead.
Some other countries are still using RSA iirc.