Griffiths arrived at Aden International Airport amid heavy security deployment and headed immediately to the Presidential Palace to hold a meeting with the country's President Abdu-Rabbu Mansour Hadi and other high-ranking government officials.
According to the government source, Griffiths might broker a ceasefire and discuss the results of his talks with Houthis.
Last week, Griffiths held similar meetings with Houthi leaders in the country's capital Sanaa, but reached no constructive outcomes regarding the rebels' withdrawal from Hodeidah.
The Yemeni Houthis have stated last week that they had struck a Saudi-US warship near the port of Al Hodeidah.
The UN and other aid groups have over the past days withdrawn their staff members from the port city in the wake of UAE threats.
The United Nations Children’s Fund (UNICEF) has also raised alarm over the impact of the attack on children in Hudaydah and beyond.
Saudi Arabia and its regional allies attacked Yemen in March 2015 to bring back to power the deposed president of Yemen Abdrabbuh Mansour Hadi.
Thousands of Yemenis have been killed in the attacks conducted by the Saudi-US coalition and more than 2,000 have died due to a cholera epidemic.
