During his two-day visit, Griffiths held a series of meetings with the Houthi leaders, including the rebel chief Abdulmalik al-Houthi and head of the group's highest revolutionary committee Mohammed Ali al-Houthi.
The Houthi-controlled Saba news agency said the meetings discussed the "obstacles and breaches" to the UN-brokered first-round peace agreement reached last month between the Yemeni rival parties in Stockholm.
They also discussed preparations to hold the second round of peace talks, Saba reported without giving further details.
Mohammed Ali al-Houthi tweeted that "no date and place have been set yet for the next round of talks."
"We demand the pay of salaries to all state employees and consider the refusal of paying the military and security institutions as the first step of an American conspiracy that seek to dissolve the Yemeni army and security institution as they did in a post-Saddam Iraq which we will never accept," al-Houthi said.
He said that his group also demands the re-opening of Sanaa airport and lift the all-out blockade on the rebel-held northern territories.
However, Griffiths' office has not released any statement to comment on his meetings.
Griffiths is also due to meet with Yemeni President Abd-Rabbu Mansour Hadi and his government in the Saudi capital of Riyadh, according to a UN statement released on Friday.
The warring forces continued to blame each other for breaching the truce in the Red Sea port city of Hodeidah and undermining the ongoing peace process.
Last week, the Houthi group said it began withdrawing from the Hodeidah ports in order to "implement the first phase of re-deployment."
In response, the UN said the redeployment "would only be credible if all parties and the United Nations are able to observe and verify that it is in line with the Stockholm agreement."
Patrick Cammaert, appointed by the UN as head of the Redeployment Coordination Committee (RCC) which includes representatives from Yemeni rival forces, would arrange the redeployment plans and mechanism required to monitor the cease-fire and ensure that "credible redeployment is achieved," it added.
Cammaert arrived in Hodeidah last week to oversee the implementation of the cease-fire between the Yemeni parties.
Under the truce, the withdrawal from the ports of Hodeidah, Salif and Ras Issa, and critical parts of the city associated with humanitarian facilities should be completed within two weeks after the cease-fire enters into force, while the full withdrawal should be completed within a maximum period of 21 days.
Saudi Arabia has been leading an Arab military coalition in Yemen against the Iran-backed Houthi militia since March 2015, in order to reinstate the exiled Yemeni government of Hadi.