Khaled al-Yamani, who took over the post in May 2018, said he would step down after some officials in the government of Abd-Rabbu Mansour Hadi faulted him for not criticizing United Nations special envoy Martin Griffiths' performance.
The resignation needs to be accepted by Hadi, who last month complained in a letter to the U.N. secretary-general that Griffiths was "legitimizing" the Houthi movement locked in a four-year war with a Saudi-led coalition loyal to the president.
"He (Yamani) was expecting to be dismissed and so he submitted his resignation before that happens," one source said.
Yamani could not immediately be reached for comment.
In his letter to Secretary-General Antonio Guterres, Hadi said Griffiths had failed to properly oversee the agreement for a ceasefire and troop withdrawal in Hodeidah, which became the focus of the war last year when the coalition tried to seize the Houthi-held Red Sea port.
The pact reached in December, the first significant breakthrough in peacemaking in over four years, had stalled for months until the Iran-aligned Houthis, who ousted Hadi from power in the capital Sanaa in late 2014, last month quit three ports in Hodeidah in a unilateral move.
The coalition has yet to verify the withdrawal or meet it by pulling back its own forces massed on the edges of Hodeidah ahead of a wider redeployment by both sides in a second phase.
The Houthis recently stepped up drone attacks on Saudi cities following a lull last year ahead of the December talks.
A U.N. official is expected to visit Saudi Arabia this week for talks with Saudi and Yemeni officials. Hadi's government is now based in Yemen's southern port of Aden.
Hodeidah handles the bulk of Yemen's commercial and aid imports and is a lifeline for millions of people at risk of starvation in the impoverished Arabian Peninsula nation.The Western-backed, Sunni Muslim Arab alliance intervened in Yemen in 2015 to try to restore Hadi's government to power in a conflict that has killed tens of thousands of people. The Houthis say their revolution is against corruption.