The UN’s special envoy for Yemen has given the security council a relatively positive view of the conflict there after the signing of a peace agreement – an assessment that contrasts with that of the UN-recognised government.

Martin Griffiths told the UN security council there had been “a significant decrease in hostilities” in Yemen since the parties signed an outline peace agreement in Stockholm last month.

His assessment that the ceasefire terms were largely being honoured by both sides follows a visit this week to Yemen, a country ravaged by civil war and repeated mass food shortages.

The envoy’s optimism was balanced by a call for greater momentum in implementing the agreement and an admission that substantial progress is needed for the next stage of the peace talks to proceed. He said that overall the violence was remarkably limited compared with before the Stockholm talks.

His view jars with claims by the UN-recognised government of Abd Rabbu Mansour Hadi that Houthi rebels have refused to abide by key aspects of the deal, including the opening of vital aid routes. The Hadi government also claims that the promised unfettered humanitarian access to the Red Sea port of Hodeidah and its surrounding flour mills has not happened.

The UN humanitarian co-ordinator Martin Lowcock told the security council: “Enough grain for 3.5 million people has now been sitting unused, possibly spoiling, for nearly four months in the mills. Unfortunately, over the last six weeks de facto authorities have blocked humanitarian supplies travelling from areas under their control to government-held areas. They have also recently informed humanitarian agencies that 72 hours’ notice is required ahead of any movements instead of the usual 48 hours.” Commercial food imports have fallen.

That assessment is shared by the Hadi government’s backers – the United Arab Emirates and Saudi Arabia.

A central aspect of the Stockholm agreement was a Houthi handover of the port to a UN-administered oversight team, the introduction of new security across the port city and a phased ceasefire across the region. A retired UN general, Patrick Cammaert, is in Hodeidah trying to implement the ceasefire, including mediating on the disagreements over the identity of the new security force.

The general’s mandate expires on 20 January, requiring a further UN mandate. The UN is also looking for agreement to introduce as many as 75 observers to monitor the ceasefire for six months in Hodeidah.

Griffiths said further talks on a prisoner swap agreement would be held in Amman, Jordan, next week.

Agreement also remains elusive on the opening of Sana’a airport to international traffic and the future of the Central Bank of Yemen.

Lowcock said the rial had slumped in value since the Stockholm talks despite a one-off cash injection.

He told the 15-member security council: “I cannot yet report to you that the wider humanitarian situation in Yemen is any better. It remains catastrophic. More than 24 million people now need humanitarian assistance – that’s 80% of the population. They include 10 million people just a step away from famine. More than 3.3 million people have been displaced – over 600,000 of them in the last 12 months.”

Most security council members decided to focus on the progress, but the German ambassador to the UN, Christoph Heusgen, described the position at the mills and ports as a scandal, adding: “We must do everything to stop this.”