The powers and tasks of the new EU leader have yet to be defined, and agreeing to a candidate is linked to negotiations on filling the other open jobs, including the foreign policy role and 25 other commissioners.
The president, who needs to be elected unanimously, will serve a two-and-a-half-year term, strengthening the current system of a six-month presidency that states hold in turn.
The creation of the posts will happen only if the Czech Republic ratifies the treaty, with the other 26 EU countries already having done so.
The leaders will need to work to overcome the refusal by Vaclav Klaus, the Czech president, to sign the treaty until his country is offered an opt-out clause from the document's Charter of Fundamental Rights.
Envoys are said to be drafting a last-minute amendment for Klaus, who has voiced concern, along with Slovakia, that the charter could be used by ethnic Germans to reclaim land they lost in the Czech Republic after the second world war.