(a) An employee of an Executive agency or an individual employed by the government of the District of Columbia who, on original appointment, subscribed to the oath of office required by section 3331 of this title is not required to renew the oath because of a change in status so long as his service is continuous in the agency in which he is employed, unless, in the opinion of the head of the Executive agency, the Secretary of a military department with respect to an employee of his department, or the Commissioners of the District of Columbia, the public interest so requires.

(b) An individual who, on appointment as an employee of a House of Congress, subscribed to the oath of office required by section 3331 of this title is not required to renew the oath so long as his service as an employee of that House of Congress is continuous.