The two-month ceasefire, which went into effect on April 2, coinciding with the start of the Muslim holy month of Ramadan, has made a “considerable positive impact on the daily lives of many Yemenis,” Grundberg said.
But he added that he was seeing unconfirmed reports of continuing armed clashes that were causing civilian casualties.
According to United Nations figures, more than 150,000 people have died in Yemen’s war and millions have been displaced.
The conflict pits Yemen’s Saudi-supported government, officially based in  the southern port of Aden, against the Iran-backed Houthis.
The Houthis seized the capital Sanaa in 2014, prompting a Saudi-led military intervention the following year and igniting a war that has caused what the United Nations terms the world’s worst humanitarian crisis.
As part of the truce, the first commercial flight in nearly six years took off from Yemen’s rebel-held capital Monday.