"The Secretary [Kerry] stressed the importance of implementing a 72-hour ceasefire by all sides to provide space for the UN Special Envoy, Ismail Ould Cheikh Ahmed, to engage in consultations with both sides," the release stated. "The Saudis agreed, provided it is implemented by all sides."
Additionally, the three officials discussed the ongoing conflict in Syria as well as the situation in Libya, the release noted.
Last week, Ahmed warned the UN Security Council that extremist groups such as al-Qaeda and the Islamic State could find a foothold in Libya if the conflict continues.
UN-brokered talks that began on April 21 ended in early August with the two sides failing to come to an agreement.
Since March 2015, the Saudi-led coalition of mostly Persian Gulf countries has been carrying out airstrikes against the Houthi rebels at the request of President Abd Rabbuh Mansour Hadi.