The report, sent to the members of the UN Security Council, also criticized Syria for allowing weapons smuggling to Lebanese militias.
Ban's report deals with Security Council Resolution 1559 of September 2004, drafted by UN Middle East envoy Terje Roed-Larsen, which called for Syria's military withdrawal from Lebanon as well as Hezbollah's disarmament.
Following the February 2005 assassination of former Lebanese prime minister Rafik Hariri, rumored to have been carried out with Syrian involvement, Syrian forces withdrew from Lebanon after decades of occupation.
That resolution formed the foundation for Security Council Resolution 1701, which ended the 2006 Second Lebanon War between Israel and Hezbollah.
Ban's report indicates that Hezbollah continues to maintain a militia separate from the Lebanese government.
"Hezbollah's maintenance of a major armed component and a para-military infrastructure separate from the state, including a secure network of communication, which the group itself deems an integral part of its arsenal, is a direct challenge to the authority of the government of Lebanon and its security forces and prevents their exclusive control over the entire territory of Lebanon," said the report.
"I therefore reiterate my call on Hezbollah to comply with all relevant Security Council resolutions, and urge all parties which maintain close ties with Hezbollah and have the ability to influence it, in particular Syria and Iran, to support its transformation into a political party proper," it said.
The report also cited the "the urgency and importance of ensuring that the Government has the monopoly on the use of force in Lebanon."
Ban also leveled criticism at the remarks made by GOC Northern Command Gadi Eisenkot to the daily Yedioth Ahronoth several weeks ago regarding the Israel Defense Forces' plans to use "disproportionate force" should war again break out with Lebanon or Hezbollah.
In response, senior Hezbollah figures told the media the organization would respond forcefully to any Israeli attack.
"I am disturbed by the repeated exchanges of threats, through the media, between Israel and Hezbollah. I urge all parties to cease this public discourse, which creates anxiety among civilian populations on both sides," he said.
Regarding weapons smuggling from Syria to Lebanon, Ban said, "Preventing breaches of the arms embargo is a critical element for strengthening Lebanon's sovereignty, territorial integrity, unity and political independence. I remain concerned by the general porosity of the Syrian-Lebanese border."
The UN secretary general also criticized Israel for its continued overflights on Lebanese territory, which Jerusalem states are necessary for security reasons.
He also stated that in recent weeks the Lebanese army transferred a significant number of troops from the Israeli border to the north of the country due to the increasing activity of international Islamic extremist groups in the coastal city of Tripoli.
"I am gravely concerned by the emergence and apparent strengthening of extremist elements and foreign fighters based largely in and around Tripoli. This phenomenon is but another challenge to the consolidation of the government's authority," he said.