"It turns out that there are parts of Jerusalem that Israel is not sovereign over and does not control – and it's happening right here in Jerusalem, the capital of Israel," Ariel said during a tour of East Jerusalem's Arab Shuafat neighborhood.
"[The solution] requires a special effort by all of us and I will work with other members to exercise their sovereignty in this area," Israeli news website Ynet quoted Ariel as saying.
"The lack of enforcing the construction regulations [here] is seen in other areas, such as security, and there are lots of illegal aliens and weapons caches," the minister added.
Palestinians want East Jerusalem as the capital of a Palestinian State that is currently "under occupation."
Israel, on the other hand, considers Jerusalem in its entirety as the capital of the self-proclaimed Jewish state.
Tension has run high in the occupied West Bank and East Jerusalem since late October, when Israel briefly closed the flashpoint Al-Aqsa Mosque compound after an extremist rabbi was injured in a drive-by shooting in West Jerusalem.
Unrest mounted further in the occupied city when Israeli forces killed a young Palestinian man – in a raid on his East Jerusalem home – who had been suspected of shooting the rabbi.
The situation escalated earlier this month when Ziad Abu Ein, a Palestinian official in charge of the Israeli settlements file at the Palestine Liberation Organization (PLO), died when Israeli troops dispersed a demonstration against the expansion of Jewish-only settlements in the West Bank.
Israel occupied East Jerusalem and the West Bank during the 1967 Middle East War. It later annexed the holy city in 1980, claiming it as its capital in a move never recognized by the international community.