The UN "strongly condemned" a recent Houthi attack that killed 10 pro-government soldiers in Taez in a statement on Wednesday evening.
The comments from Hans Grunberg calling on all sides to respect the ceasefire in the country came after Yemeni officials called on the international body to denounce the violation of the truce.
On Monday, the Iran-backed rebels launched an offensive in Al Dhabab near the southern city of Taez, which has been under Houthi siege for seven years. The Yemeni government said the assault killed 10 soldiers and aimed to "cut the only lifeline route connecting the City of Taez to Aden governorate" which has become the de facto capital after Sanaa was taken by the rebels in 2015.
Under the UN-brokered ceasefire that came into effect on April 2, the Houthis have agreed to open the roads to the city to end the siege but this has not yet taken place.
Mr Grundberg said the latest incident "threatens to seriously worsen the humanitarian situation for civilians".
"I call on the parties to seize the opportunity provided by the truce extension to demonstrate full commitment to ending the prolonged conflict in Yemen and the suffering of its people, as well as engage with my office to continue discussions to meet the obligations they made under the truce," said Mr Grundberg.
"My efforts will continue to work with the parties to navigate the path toward reaching a comprehensive political and peaceful settlement of the conflict."
Earlier, pro-government Yemenis called on the UN to insist the Houthi rebels also refrain from military escalation around the Red Sea city of Hodeidah.
On Tuesday, the UN Mission to support the Hodeidah Agreement said it "observed with great concern the significant military presence" of Houthi militants in the port city in the past days.
In 2019, the UN brokered a deal to avert a massive government offensive to capture the strategic port city. Under the terms, all sides would pull back from Hodeidah and hand the city over to a local security force while international agencies oversaw the port that is a vital lifeline for much of northern and central Yemen. The deal has only partly been implemented with the government stepping back but the rebels remain in control of the town.
Despite the UN's criticism of the Houthi mobilisation in Hodeidah, officials and pro-government activists still accused the international body of leniency towards the rebels.
On Tuesday, Yemen's Parliament Speaker Sheikh Sultan Al Barakani met Mr Grundberg to discuss the recent developments.
Mr Al Barakani said the Houthis "are not serious in dealing with the peace process, given that they had committed hundreds of violations to the UN truce, including the attack on Taez", state news agency Saba reported.
"The Houthi militia are not a partner in making peace," the Parliament Speaker said.
"We call on the UN envoy and international community to shoulder their responsibility to deter the Houthi militia."
Activist Fahad Al Khlefi called Monday's incident "a fully formed crime", and not a mere breach of the truce.
The British Ambassador to Yemen said he was "deeply troubled" by the Houthi attack.
"I urge all parties to engage with the UN-facilitated Military Coordination Committee which aims to de-escalate. The Truce is delivering for Yemenis. All parties must embrace it as an opportunity for peace," said Richard Oppenheim.
Taez has been under Houthi siege for seven years and remains a major sticking point for the warring parties in reaching a political agreement to end the war.
The UN and the Yemeni government have repeatedly called on the Houthis to reopen roads in and around Taez to allow much-needed aid to flow in and alleviate people's suffering by improving mobility out of the governorate.
A military committee engaged in UN-brokered talks with the Houthis in the Jordanian capital, Amman, also said it has suspended negotiations "until further notice" due to the Houthi breach of the truce.