Nasrallah also said "legitimate questions" were being raised in Lebanon over whether Hariri was being detained in Saudi Arabia.
Speaking to the Lebanese television channel LBC, Sabhan said Hariri is completely free to return to Lebanon, adding, however: "We do not want explosions and destruction to happen again in the Hariri family".
In a televised address on Saturday, Prime Minister Hariri announced an unexpected resignation saying the atmosphere in the country resembles that before the assassination of his father, former Lebanese Prime Minister Rafic Hariri, who was killed in 2005.
Nasrallah said he would not comment on accusations levelled against Hezbollah by Hariri, describing his resignation announcement as a Saudi statement.
Hariri became prime minister in late 2016 in a coalition government that included the Shiite militant group Hezbollah, one of Saudi Arabia's chief detractors in the region.
Sunni Muslim Saudi Arabia, a political ally of Hariri, is locked in a bitter tussle for power across the Middle East with Shi'ite Iran and its allies, including Hezbollah. The nation was without a cohesive government and leadership for almost two years.
His father, Rafik al-Hariri, was prime minister after Lebanon's 1975-1990 civil war and was assassinated in a vehicle bombing in 2005. Hezbollah is considered a terrorist organization by a number of countries including the United States, Israel, and the United Kingdom.
According to the source, with their inappropriate demands, Hariri and the Saudis expected Iran to leave alone the Yemenis to their fate "but after receiving Iran's negative response, the Saudis called back Hariri and urged him to resign".
In this February 14, 2005, file photo, vehicles burn following a massive bomb attack that tore through the motorcade of former Prime Minister Rafik Hariri in Beirut, Lebanon.