"Both sides have largely adhered to the ceasefire we agreed in Stockholm on the Al Hudaydah governorate, and there has been a significant decrease in violence since then," Dujarric said.
The spokesman hailed the progress that has been made since the warring parties agreed to the deal inked in Sweden.
The next steps in resolving the crisis in Yemen should include prisoner exchanges and an effort to address the ongoing violence in Taiz, Dujarric said.
The remarks come after, earlier in the day, the United Nations Security Council (UNSC) held a meeting on Yemen to discuss the implementation of the Stockholm Agreement.
Later in the month, the UN Security Council adopted a resolution calling for a 30-day deployment of a United Nations team to Yemen to help monitor the ceasefire.
Yemen has been ravaged by almost four years of war between the internationally backed government, supported by the Saudi-led coalition, and the Houthi rebels.