Hezbollah's arsenal has been at the centre of the dialogue, stalled since 2010 because of bickering between rival parties.
The powerful Shiite group, which dominates the government and is blacklisted as a terrorist organisation by Washington, has steadfastly refused to abandon its weapons, arguing they are needed to defend Lebanon against Israel.
Ban also confirmed at the news conference that the mandate of a controversial UN-backed court that has charged four Hezbollah operatives with the 2005 assassination of ex-premier Rafiq Hariri would be extended.
He said he had discussed the matter earlier on Friday in meetings with Sleiman, Prime Minister Najib Mikati and parliament speaker Nabih Berri.
"How long the mandate will be extended will be (decided) in consultation with the Lebanese government and Security Council," he said.
The mandate of the Netherlands-based Special Tribunal for Lebanon (STL) expires on February 29.
Hezbollah last January toppled the government of Saad Hariri, the slain leader's son, after he refused to cut ties with the tribunal.
His successor Mikati, appointed with the blessing of Hezbollah, has had to manoeuvre carefully in dealing with the STL, denounced by the militant group as a US-Israeli tool.
Asked whether he would meet any officials from Hezbollah, which has two ministers in the government, Ban said "we will see."
He said he had also addressed in his meetings with Lebanese officials the uprising in neighbouring Syria and its potential impact on Lebanon.
He did not elaborate, but in an interview with the Lebanese Arabic-language daily An-Nahar ahead of his visit, Ban urged the international community to adopt a united stand on Syria.
He said he had repeatedly appealed to Syrian President Bashar al-Assad to stop the bloodshed that has left more than 5,000 people dead, but that Assad had made only empty promises.
Syrian troops have killed six people since October in now-regular incursions into Lebanon, where they have opened fire on border villages.
Lebanon and Syria share a 330-kilometre (205-mile) border, but have yet to agree on official demarcation, an issue that was the topic of talks between Ban and Mikati.
"The Lebanese government's priority is to maintain stability in Lebanon and avoid repercussions" of the Syria crisis, read a statement from Mikati's office.
Ban on Saturday was to inspect troops serving with the UN peacekeeping force in southern Lebanon (UNIFIL), which has been the target of a string of attacks in the past year and is now under a "strategy" review by the United Nations.
A statement released by Sleiman's office said the president had conveyed to Ban his hope that the size and mandate of the force would not be reduced.
Ban was also to meet members of the Western-backed opposition.
Several dozen people had gathered in downtown Beirut on the UN chief's arrival to express their support for Hezbollah and Assad's embattled regime.