The Saudi move on Friday sparked disarray at the council, where it only won the seat at a UN General Assembly election the previous day.
Russia criticised the Saudis' "strange" decision, but the conservative kingdom got a more understanding reaction from western nations.
UN leader Ban Ki-moon said Saudi Arabia did not immediately send notification of its decision to reject the term due to start on January 1, and diplomats say it could be possible to persuade the Saudi government to reverse the decision.
The Saudi foreign ministry announced the decision in a statement that said "work mechanisms and double-standards on the Security Council prevent it from carrying out its duties".
"Therefore, Saudi Arabia... has no other option but to turn down Security Council membership until it is reformed and given the means to accomplish its duties and assume its responsibilities in preserving the world's peace and security."
The government said "allowing the ruling regime in Syria to kill and burn its people" with chemical weapons is "irrefutable evidence and proof of the inability of the Security Council to carry out its duties and responsibilities".
Saudi Arabia was one of five nations elected by the UN General Assembly on Thursday to start a two-year term on the Security Council. The others were Chad, Chile, Lithuania and Nigeria. All had stood unopposed.
No country has ever won a council seat and then refused to take it up.
Saudi Arabia's UN ambassador, Abdullah Al-Mouallimi, gave several press interviews hailing the election, but the celebrations had barely finished when the withdrawal was announced.
If Saudi Arabia maintains the threat, the Asia-Pacific group of nations would have to propose a new candidate for the UN General Assembly to vote on.
Amid the diplomatic disarray, the decision again highlighted international divisions over the Syria conflict.
The Russian foreign ministry sharply criticised Saudi Arabia's argument on the council's record on Syria, saying it "arouse bewilderment".
However, France said several countries share Saudi Arabia's frustration.
"We think that Saudi Arabia would have brought a very positive contribution to the Security Council, but we do also understand the frustration of Saudi Arabia," France's UN ambassador Gerard Araud told reporters.
"The fact is that the Security Council has been unable to act now for more than two years."Do you have any story leads, photos or videos?