A presidential statement approved by all 15 council members was aimed especially at President Salva Kiir, who signed the deal reluctantly and with reservations on Wednesday.
Rebel leader and ex-vice president Riek Machar signed on August 17 without reservations. The Security Council quickly threatened sanctions after Kiir refused to sign at the time.
The council statement welcomed the signatures but expressed concern "with any statement by any party suggesting a lack of commitment to implement the agreement."
The violence has killed thousands, created a humanitarian crisis and displaced over two million people, including almost 200,000 still taking refuge at UN peacekeeping sites.
The Security Council statement called the peace agreement "the first step in reversing the difficult political and economic situation, and humanitarian and security catastrophe resulting from this crisis."
The agreement gives the sides 72 hours from signing to implement a cease-fire. It calls for a transitional government to be established within 90 days. Machar is widely expected to return as Kiir's deputy.
It also underscored "the pressing need to ensure accountability for serious violations and abuses of human rights and serious violations of international law" during the conflict.
