"The secretary general regrets that the Lebanese parliament was unable to elect a new president within the timeframe set by the constitution. He calls on the country's leaders to engage intensively to ensure the election of a new president without delay," Xinhua quoted his spokesperson as saying in a statement.
The secretary general also called on "Lebanese leaders to ensure the continued effective functioning of the institutions of the state, to guarantee that the government is able to address the challenges facing the country and to meet Lebanon's international obligations".
"The United Nations remains committed to continued partnership with the Government of Lebanon as it works towards achieving these goals," said the statement.
The term of the current head of state, Michel Sleiman, ended on Sunday, and the Lebanese Constitution specifies that parliament members must convene to elect a new president before the deadline passes.
Ban paid tribute to the leadership demonstrated by President Sleiman over the past six years and lauded "his commitment to the unity and stability of Lebanon".
Earlier in the month, after meeting with Speaker of the Parliament, Nabih Berri, the UN special coordinator for Lebanon, Derek Plumbly, said the country should avoid a vacuum in the presidency.
"We earnestly hope that members of parliament will engage fully in the coming days to secure the election of a president by the date set in law," Plumbly said in the capital Beirut.
Lebanon has been split between two major opposing camps, resulting in a political deadlock throughout the government. The March 8 camp backs President Bashar al-Assad of neighbouring Syria, while members of the March 14 camp oppose the Syrian government and support rebels in their fight against Assad.