Who can initiate an optional referendum at the national level?

Iceland's Constitution (1944, last amended in 2013)

Article 26.

If Althingi has passed a bill, it shall be submitted to the President of the Republic for confirmation not later than two weeks after it has been passed. Such confirmation gives it the force of law. If the President rejects a bill, it shall nevertheless become valid but shall, as soon as circumstances permit, be submitted to a vote by secret ballot of all those eligible to vote, for approval or rejection. The law shall become void if rejected, but otherwise retains its force.

Act on the implementation of referendums (2010, amended in 2011)

Article 1. Álykti Alþingi að fram skuli fara almenn og leynileg þjóðaratkvæðagreiðsla um tiltekið málefni eða lagafrumvarp fer um framkvæmdina samkvæmt lögum þessum. Niðurstaða slíkrar atkvæðagreiðslu er ráðgefandi.