Mokha's capture brings the Iran-backed group closer to controlling a key international shipping route.
The paper said it stood by its reporting, after publishing extracts from a book where the claim appears.
The Algerian foreign ministry did not give a reason for the move but said it had exhausted all means.
The president also said oil prices won't come down until after the November races, claiming without evidence that Iran wants to impact the election.
BBC's Middle East Correspondent Lucy Williamson visits the Palestinian community of Khan al Ahmar in the so-called E1 area, and the neighbouring Israeli settlement of Maale Admumim.
The UK accuses Israel's government of turning a blind eye to the "ethnic cleansing" of Palestinians by settlers.
The foreign secretary disagrees that sanctions on Israeli settlements could put British Jews at greater risk.
Tehran condemns the resolution, blaming US and Israeli strikes on its nuclear facilities for disrupting inspections.
Brent crude - the global benchmark for prices - rises after the US hit five Iranian tankers on Tuesday
Britain's foreign secretary accuses settlers of carrying out the "ethnic cleansing" of Palestinians, as Israel responds by shutting the UK consulate in East Jerusalem.