Residents in Hodeidah are cautiously hoping that the Yemeni city will be spared future bloodshed as a long-awaited withdrawal by Houthi rebel forces appeared to be proceeding according to plan.

The four-day redeployment process had been a success, residents told the Guardian, although there were reports of sporadic violence on the city’s eastern outskirts on Monday evening.

The Houthi withdrawal is an important first step in a complex de-escalation plan agreed in ceasefire talks in the civil war between the rebels and Yemeni government held in Sweden at the end of last year.

It comes ahead of a meeting this week of the UN Security Council at which it was expected Britain and the US were preparing to criticise the Houthis for failing to help the UN special envoy for Yemen, Martin Griffiths, implement the agreements reached in December at a breakthrough meeting in Stockholm.

“We are very tired of the situation to date,” said Dr Abdel al-Montaser, a Hodeidah resident. “Most people are optimistic, especially as this is happening during the holy month [Ramadan].”

Yemen’s coast guard has taken over responsibility for security at the three ports, Lt Gen Michael Lollesgaard, the head of the UN’s Redeployment Coordination Committee, said in a statement. De-mining operations and the removal of military equipment are expected to take place in the next few days.

Hodeidah, which is home to about 600,000 people, is Yemen’s second largest city by population. Its vital port – through which 70% of Yemen’s food, fuel and aid flows – has been under Houthi control since 2015 and has become the country’s major aid pipeline due to the Saudi-led coalition blockade of Yemen’s borders and airspace.

The city has twice been threatened by a full-scale offensive by coalition forces fighting to restore Yemen’s government, although aid agencies have repeatedly warned that any damage to the city’s port or delays in aid delivery will tip the country into a full-blown famine.

Currently, three quarters of Yemen’s 28-million population is dependent on aid to survive, and about 14 million people do not have enough to eat.

“The situation here in Hodeidah has been very grim, very unstable,” said a resident who asked not to be named for fear of Houthi reprisals.

“We are still afraid and there is not enough food. The Houthis recently began forcing children to fight and if the parents refused they were threatened with death. I hope to God this is a turning point.”

Trust is still sorely lacking between Yemen’s warring parties and threatens to derail the peace process: Yemeni government official say that the Houthi withdrawal was a ploy designed to “fool the international community” and have accused the rebels of putting their fighters in neutral coast guard and police uniforms in order to keep control of the ports.

The Houthis have denied the accusations, saying in a statement that the unilateral pullout from Hodeidah shows their commitment to the peace process goals set out in Stockholm last year.

However, fierce fighting continues in other parts of the country, and tensions between Iran, which backs the Houthi rebels, and Saudi Arabia, which spearheads the coalition fighting to restore Yemen’s government, have skyrocketed in recent days after Houthi claims of responsibility for attacks on Saudi oil tankers and an oil pipeline.

“There are no alternatives at present to making December’s Stockholm agreement work. Further consultations towards peace are urgently required, but the next round was only set to happen after real progress had been made in implementing [Stockholm],” said Dr Elisabeth Kendall, a researcher at Oxford University.

“The hope is that, if the Houthi withdrawal is genuine, then it removes the impediment to further talks. That in turn gives a chance for the UN to feel out further measures that could build trust and ultimately make some progress on the long road to peace.”

But the Yemeni government information minister, Moammar al-Eryani, told the Guardian the Houthi withdrawal was a “comedy” and deception, as he challenged the Houthis to allow civilians to monitor the withdrawal in line with agreements reached with the UN.

El-Eryani said: “We support the work of Martin Griffiths, but he is just trying to achieve any kind of success, but unfortunately no success could be achieved with the Houthis. It was just delusional. The truth will be revealed very soon. The Houthis will not have withdrawn, they are not going to hand over the maps showing the mines, there will be no withdrawal of military manifestation and they will not allow for this verification of the troop withdrawal.

“If they allowed it for a time they will not allow it to continue.”

He said the Houthis were only acting under duress and the fear of the upcoming UN security council meeting.

He also claimed Houthis had installed surveillance cameras and brought more troops under the guise they are the coastal guard. “This is an organisation that has not honoured an agreement since 2004.”

The Houthis have been reluctant to withdraw if the civilian force that takes over is largely filled with Yemen government officers.