The United Nations special envoy to Yemen and the country's foreign minister discussed plans to secure the release of prisoners from Houthi controlled jails at a meeting in Riyadh on Monday.
Yemeni Foreign Minister Khaled Al Yamani briefed the UN envoy on the progress in releasing all of the prisoners captured by Houthi rebels, the pro-government Saba news agency reported.
The release of prisoners is seen as the first step in building trust between the internationally recognised Yemeni government and the Houthi militants.
It is unclear if they discussed the release of Houthi prisoners.
Mr Yamani and Mr Griffiths also discussed confidence-building measures and ending the humanitarian crisis in the country.
The foreign minister called for co-operation with the United Nations on supporting the Central Bank of Yemen, which is struggling to control a deteriorating currency and high inflation.
The military operation in the Hodeidah was avoiding civilian casualties as a priority, Mr Yamani said, in an attempt to quell international fears.
“The military operations are moving ahead steadily and carefully to safeguard civilian lives,” he said, according to Asharq Al Awsat.
Hodeidah is a key strategic port in the country, acting as the entry point for 70 to 80 per cent of the country's food and medicine.
Mr Yamani also spoke to representatives from the US and France, the newspaper reported.
Mr Griffiths will brief the UN Security Council on November 16 and hopes to restart peace talks within a month, after they collapsed in Geneva in September following the failure of Houthi rebels to attend the negotiations.
On Monday, Yemen's former prime minister said a peace deal is still possible, but stressed the rebels are running out of opportunities for a resolution.
"If they delay the peace process [again], then they will lose everything and the international community will deal with them as a terrorist organisation just like ISIS," Mr Bahah told The National on the sidelines of the Abu Dhabi Strategic Debate conference.
The Yemeni conflict began in 2014 when Houthi rebels invaded the capital Sanaa, toppling the internationally-recognised government of President Abdrabu Mansur Hadi.
An Arab coalition intervened in March 2015 at Mr Hadi's request. The conflict has killed thousands and created a humanitarian crisis for the hundreds of thousands of Yemenis still trapped in the country.
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