Britain’s foreign secretary has begun a three-day visit to the Middle East in an effort to salvage Yemen’s faltering ceasefire, telling Houthi rebels they must start withdrawing their forces from the port of Hodeidah in line with a UN peace plan.

Jeremy Hunt is also under political pressure at home to take a tougher line on his trip with Saudi Arabia over the murder of the Washington Post journalist Jamal Khashoggi.

Hunt met the Houthi movement’s chief negotiator, Mohamed Abdul-Salam, in Oman, telling him the withdrawal of troops from Hodeidah needed to happen soon to maintain confidence in the UN cessation of hostilities agreed in Sweden in December. The Hodeidah agreement will allow the opening of vital humanitarian channels.

The UK is concerned that perceived Houthi delaying tactics may lead Saudi Arabia and the United Arab Emirates to return to a military solution to the four-year Yemen civil war.

Yemeni pro-government soldiers stand next to tanks near Hodeidah. Photograph: Najeeb Almahboobi/EPA

Saudi Arabia has been backing a UN-recognised Yemen government in its efforts to recapture the country, including the capital, Sana’a.

An outline agreement on the redeployment of Houthi and government forces was agreed at UN talks in Rimbo near Stockholm, but repeated rows over the sequencing of the withdrawals has delayed progress.

Fighting between government forces and Houthi fighters has continued outside the ceasefire areas.

The Stockholm agreement provided for the troops’ mutual withdrawal in two phases, starting from the ports of Ras Isa, Saleef and Hodeidah’s main port, and concluding with full withdrawal from inside and around Hodeidah city under the supervision of the head of the UN observer mission in the country, Gen Michael Lollesgaard.

The deadline for implementing the first phase , already postponed once, passed on Thursday without Houthi militia withdrawing from either Saleef or Ras Isa. The dispute is tied to disagreements over the nature of the local force that would police Hodeidah city after the withdrawals.

The Yemeni foreign minister, Khaled al-Yamani, called on Lollesgaard and the UN special envoy for Yemen, Martin Griffiths, to denounce what he described as “the rebels’ stalling and intransigence, and … their open deception of the UN and the international community”.

The UN is determined to keep its lines open to both sides and has not attributed blame for the delays. The Houthi movement has listed as many as 600 breaches of the ceasefire by the Saudi-led coalition forces supporting the government.

A team from the World Food Programme visit mills in Hodeidah. Photograph: EPA

Houthi fighters did allow a UN aid team access to the mills in Hodeidah, where about 51,000 tonnes of grain aid, enough to feed 3 million Yemenis, are stored.

Hunt, who has travelled to the region twice recently to help the peace efforts, as well as flying to Sweden for the talks in December, is scheduled to travel to Riyadh and Dubai.

British sources said it appeared as if Houthi negotiators were the side least willing to implement the Stockholm agreement, although the main obstacle is lack of trust between the parties.

In Riyadh, Hunt is to meet the new Saudi foreign minister, Ibrahim al-Assaf, who was appointed after Khashoggi’s murder.

Britain, which is historically close to Saudi Arabia, appears to be focussing on Yemen rather than demanding progress in the investigation into the killing of the journalist at the Saudi consulate in Istanbul in October.

A protest holds a poster of Jamal Khashoggi outside the Saudi consulate in Istanbul

last year. Photograph: Osman Örsal/Reuters

The Saudi investigation is so shrouded in secrecy that the UN has set up its own inquiry. Shortly after the murder, the UK said Riyadh’s handling of the case would determine the nature of its future relations with Saudi Arabia.

The UK’s Foreign Office has taken three steps that will please Riyadh in the last week. It proscribed the political wing of Iranian-backed Hezbollah, vetoed European commission plans to put Saudi Arabia on a money-laundering list and pressed Berlin to resume arms sales to the country.

Hunt will also be updated on the Saudi view of the Middle East peace plan to be put forward by Jared Kushner, Donald Trump’s son-in-law and a senior White House adviser.

Kushner briefed Riyadh on his plans before traveling to Qatar this week. He is looking for a multibillion investment from the Gulf countries to fund a plan to bolster the Palestinian economy.

The Labour party claims the British government’s closeness to Saudi Arabia makes it a poor honest broker in the region.

Andrew Smith of Campaign Against Arms Trade said: “The humanitarian crisis in Yemen is the worst in the world. UK-made fighter jets and bombs have played a central role in creating it. Thousands of people have been killed by the bombs, and many more [face] catastrophe.

“Jeremy Hunt talks a lot about the need for peace, but his words are hollow. The biggest change he and his colleagues could make, and the one that would have the greatest impact on the ground, would be to finally stop arming and supporting the Saudi-led coalition.”

Efforts are still underway in the US to pass legislation ordering Trump to end US support for the coalition. A cross-party group of senators have also tabled a draft resolution that links greater Saudi transparency on the Khashoggi murder to any US cooperation with Saudi Arabia’s civilian nuclear development.