The council warned in a unanimous statement that it will "monitor the parties' compliance with the redeployment plans" as it awaits a report by UN Secretary-General Antonio Guterres on whether the sides are upholding commitments, AFP reported.
The redeployment of forces was agreed in December under a ceasefire deal reached in Sweden that offered the best hope in years of moving toward an end to the ongoing Saudi war that has killed tens of thousands and has pushed Yemen to the brink of famine.
The council expressed "grave concern" that four months on, the agreements have not been implemented, but there was no threat of sanctions against those who are blocking the peace effort.
UN envoy Martin Griffiths told the council on Monday that the ex-government and fighters from Houthi Ansarullah movement had agreed to the operational details of the first long-delayed pullback of forces from Hudaydah.
The United Nations announced a deal on the two-stage pullback from Hudaydah city and its ports in February, but the redeployment failed to materialize on the ground and the peace effort has since stalled.