Griffiths' visit is intended to send a message to the rebels, who control the Red Sea city, and the government forces, who have been attacking it with support from a Saudi-led coalition, to keep a lid on hostilities in the runup to the talks in Sweden, a UN source told AFP.
Griffiths, who arrived in the rebel-held capital Sanaa on Wednesday, met rebel chief Abdulmalik al-Houthi and addressed "what can facilitate new discussions in December", rebel spokesman Mohammed Abdelsalam said.
The conflict in Yemen, which escalated when the Saudi-led coalition intervened in 2015, has killed thousands of people and left up to 14 million at risk of famine, according to UN agencies.
In the past week, both sides have expressed support for the UN envoy's mission to relaunch peace talks, and the fighting in Hodeida has diminished despite intermittent clashes.
Under heavy Western pressure, the government and its Saudi-led military backers have largely suspended a five-month-old offensive on the Red Sea port city, which receives at least 70 percent of the country's aid.
The international community is demanding in return that the rebels halt all offensive operations, particularly missile attacks on neighbouring Saudi Arabia, and commit to joining talks on handing over of the port of Hodeida to UN control.
The World Health Organization says nearly 10,000 people - mostly civilians - have been killed in Yemen since the Saudi-led intervention began, but human rights groups believe the toll may be five times higher.
Save the Children said on Wednesday that some 85,000 infants under the age of five may have died of severe malnutrition or related diseases between March 2015 and this October based on UN agency figures.
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