Who administers direct democracy mechanisms at the national level?

According to Article 69 of the Constitution (Constitutional Amendments) and Article 59 of the Constitution (Member of Parliament Recall Elections), referenda are conducted by the Electoral Commission.  

Referendum(Amendment) Act 1992 (Enactedin 1992)

http://www.paclii.org/ki/legis/num_act/ra1992168/

Referenda to whichthis Act applies, Article 2.

This Act appliesto and in relation to ?

(1) any referendumunder Section 59 of the Constitution, whether an elected member of the Maneabani Maungatabu should vacate his seat in the Maneaba; and

(2) any referendumunder Section 69 (3) of the Constitution, as to a Bill to alter Chapter II ofthe Constitution.

Conduct of Referenda, Article 5.
(1) Subject to this section, a referendum referred to in Section 2(a) shall beconducted by the Electoral Commission in the same way as a bye-election to filla vacancy in the seat of a member of the Maneaba ni Maungatabu for theelectoral district concerned, and the Elections Ordinance and the regulations made under it, withthe necessary modifications, apply accordingly.
(2) Subject to this section, a referendum referred to in Section 2 (b) shall beconducted by the Electoral Commission (but not under the superintendence of theChief Justice) in the same way as the election of a Beretitenti, and the Election of Beretitenti Act and the regulations made under it, withthe necessary modifications, apply accordingly.
(3) In the application, by virtue of subsections (1) and (2), to a referendumof the Elections Ordinance and the Election of BeretitentiAct, and of the regulations made under them

(a)references to anelection shall be read as references to a referendum;

(b) references to an election shall beread as references to a referendum;erences to ballot papers shall be read asreferences to ballot papers containing the question for decision in thereferendum.

Result of Referenda, Article 6.

(1)As provided in Section 59(4) of theConstitution, if in a referendum referred to in Section 2 (a) a majority ofthose entitled (as set out in Section 4(1)) to vote in that referendum vote forthe removal from the Maneaba ni Maungatabu of the member named in the petition,the member shall vacate his seat forthwith.
(2) As provided in Section 69(3) of theConstitution, the Bill the subject of a referendum referred to in Section 2(b)shall not come into operation unless it is supported by the votes of not lessthan two thirds of all the persons entitled (as set out in Section 4(2)) tovote in the referendum.
(3) The result of a referendum referred to inSection 2 shall be announced by the Electoral Commission.