Al-Hariri and 22 others were killed in a bombing in Beirut in 2005, the first in a series of assassinations of anti-Syrian figures.
Lahoud, left, warned Ban of instability
if the court was set up [Reuters]
Syria has denied involvement and its Lebanese allies oppose the tribunal in its current form.
Fuad Siniora, Lebanon's prime minister, on Monday wrote to Ban asking the Security Council to consider the request.
But the pro-Syrian president and opposition in Lebanon have rejected the move.
Emile Lahoud, Lebanon's president, in his own letter to Ban, accused Siniora of "falsifying facts to drag the Security Council... into siding with one Lebanese party against the other".
He warned of instability if the council moved to set up the court that "would imply a full bypass of the constitutional mechanisms in Lebanon".
Lahoud's letter, released on Tuesday in Beirut, has not been received by the Security Council.
Nabih Berri, the parliamentary speaker, refused to call a session to ratify the tribunal.
"We cannot allow [the] killers to get away with impunity"
Zalmay Khalilzad, Security Council president
Zalmay Khalilzad, the US ambassador to the UN and current Security Council president, said he expected to introduce a draft resolution before the end of the week.
He cited "justice" and the "long-term stability of Lebanon" for wanting to move quickly.
"We cannot allow killers to get away with impunity."
Diplomats said the resolution will be sponsored by the US, Britain and France.
It remains unclear where Russia, a Syrian ally and one of five veto-wielding Security Council members, stands on the matter.