He can, as he is the authority by which it was classified (and by which it gets declassified) in the first place.
The blockbuster article in The Washington Post saying President Donald Trump had "revealed highly classified information
www.politifact.com
I have seen this claim made several times based on an Atlantic Opinion piece pointing to the fact that the relevant statute for Restricted Data lays out that the Nuclear Regulatory Commission had oversight of it, just as, for example, the NSA has oversight of SIGINT, CIA has oversight of HUMINT, the JCS has oversight of ACCMs, etc.
I found that interesting enough to go look up the Nuclear Regulatory Commissions' declassification process - and turns out, it flows from the exact same Presidential Authority as does other classification, which makes sense, given that the same statute reference is mingling discussion of nuclear data with defense data (as there is obviously overlap).
What's their declassification authority? Well, according to them, it's POTUS.
www.nrc.gov
The NRC's Declassification Process
Executive Order 13256 prescribes a uniform system for classifying, safeguarding, and declassifying national security information. (As such, this new Order replaces Executive Order 12958, which President Clinton issued in 1995 and President Bush subsequently amended in 2003.) As specified in the Executive Order, when information is originally classified (Confidential, Secret, or Top Secret), an original classification authority must establish a specific date or event for declassification based on the duration of the national security sensitivity of the information. Moreover, Section 3.1 of the Executive Order requires information to be declassified as soon as it no longer meets the standards for classification.
Under the NRC's Declassification Program, all classified documents are reviewed for automatic declassification not later than 25 years from the date of the document. Classification determinations are based upon classification guides developed by the U.S. Government. Information may only be declassified by (1) the official who authorized the original classification, (2) a supervisory official (or successor) of the originating classification authority, or (3) agency subject matter experts who have been delegated declassification authority in writing by the NRC. Information that continues to meet the classification requirements of the Executive Order warrants continued protection. Thus, in accordance with Section 3.3 of the Executive Order, NRC senior officials may exempt from automatic declassification certain specific classified information.