Griffiths told the UN Security Council last week that Yemen's parties had given "firm assurances" they were committed to attending peace talks he hopes to convene in Sweden before the end of the year.
Griffiths visited Sana’a on Thursday where he met with Houthi leaders to discuss their attendance in the next round of consultations, expected in early December.
The port city - the main gateway for imports of relief supplies and commercial goods into the country - is under Houthi control. In June, the Saudi-UAE alliance launched a wide-ranging operation to retake the strategic seaport but failed to do so.
UN agencies say up to 14 million Yemenis are at risk of starvation if the port of Hudaydah is closed by fighting or damage.
Aid group Save the Children reported on Wednesday that as many as 85,000 children may have starved to death in the past three years during Saudi Arabia's brutal war on the impoverished Arab country.