Yes, but with limitations. The government can claim adverse possession over private land only if it satisfies the same strict conditions required of any private person — i.e., actual, open, continuous, and hostile possession for at least 12 years under Article 65 of the Limitation Act, 1963. However, courts have increasingly discouraged or criticized such claims by the State.

Government as a Claimant of Adverse Possession
Traditionally, the law does not differentiate between private parties and the State when applying adverse possession. However, when the State itself wrongfully occupies private land, the courts see it as a violation of constitutional rights.

Why Courts Dislike It When the Government Claims Adverse Possession
Violates Article 300A – No person shall be deprived of property save by authority of law.
Betrays public trust – The State is supposed to protect citizen rights, not exploit legal loopholes.
Seen as an abuse of power and a denial of natural justice.
State of Haryana v. Mukesh Kumar (2011) 10 SCC 404
“The State cannot be permitted to perfect its title by adverse possession to grab the property of its citizens.”
The Supreme Court held that it is morally and constitutionally wrong for the State to invoke adverse possession against its citizens.