Answer: Patriot Act

The Patriot Act defines a terrorist organization as:

vi) Terrorist organization defined.--As used in clause (i)(VI) and clause (iv), the term `terrorist organization' means an organization--
``(I) designated under section 219;
``(II) otherwise designated, upon publication in the Federal Register, by the Secretary of State in consultation with or upon the request of the Attorney General, as a terrorist organization, after finding that the organization engages in the activities described in subclause (I), (II), or (III) of clause (iv), or that the organization provides material support to further terrorist activity; or
``(III) that is a group of two or more individuals, whether organized or not, which engages in the activities described in subclause (I), (II), or (III) of clause (iv).''
[[Page 115 STAT. 349]]

Those activities referred to in (II) are:
(I) has engaged in a terrorist activity,
(II) a consular officer or the Attorney General know or has reasonable ground to believe, is engaged in or is likely to engage after entry in any terrorist activity (as defined in clause (iv)),
(III) has, under circumstances indicating an intention to cause death or serious bodily harm, incited terrorist activity,
[[8 USC 1182(a)(3)(B)(i)]]

In short, the Secretary of State does have the power to designate groups as terrorist organizations.

This power is not extended to the Secretary of the Treasury although she or he does have the power to designate a jurisdiction as a "money laundering concern"

``(a) International Counter-Money Laundering Requirements.--
``(1) In general.--The Secretary of the Treasury may require domestic financial institutions and domestic financial agencies to take 1 or more of the special measures described in subsection (b) if the Secretary finds that reasonable grounds exist for concluding that a jurisdiction outside of the United States, 1 or more financial institutions operating outside of the United States, 1 or more classes of transactions within, or involving, a jurisdiction outside of the United States, or 1 or more types of accounts is of primary money laundering concern, in accordance with subsection (c).
[[Page 115 STAT. 298]]

If you'd like to view the full text of the Patriot Act, you can use the following link:
http://frwebgate.access.gpo.gov/cgi-bin/getdoc.cgi?dbname=107_cong_public_laws&docid=f:publ056.107
(If for some reason this doesn't work, got to http://thomas.loc.gov, click "Bills, Resolutions" on the left, under "Search Bill Summary & Status" click "Advanced Search", under "Select Congress", select 107, then under "Enter Search", select "Bill Number" under the drop-down, type H.R. 3126 in the text box, and hit search!)