Griffiths cited the firing of ballistic missiles against Saudi Arabia, intensified military operations in northwestern Saada governorate, ongoing air raids and movements of forces in the Hudaida region as worrisome developments.
"Houthis in Yemen fired a total of 119 ballistic missiles targeting Saudi Arabia so far, warning of a "painful" military response if the militants mounted any new attacks", the publication said quoting Colonel Turki al-Maliki, an Arab coalition spokesman.
Griffiths, a former British diplomat who replaced Mauritania's Ould Cheikh Ahmed as the UN Special Envoy last month, briefed the UN Security Council for the first time on Tuesday.
Yemen's internationally-recognised government said last week the drones used to attack Saudi Arabia were "made in Iran".
The Houthis have fired dozens of missiles into Saudi Arabia since a year ago, all of which were intercepted.
Al-Maliki repeated previous statements accusing Iran of providing missile components to the Houthis.
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UN diplomats say Iran, which has backed the Huthis, has signaled that it is ready to work for a settlement in Yemen, which the United Nations describes as the world s worst humanitarian crisis.
Russian Federation in February vetoed a British-drafted resolution strongly supported by the United States that would have put pressure on Iran over its failure to block supplies of missiles to the Huthi rebels.
The war has killed more than 10,000 people, displaced more than 2 million and driven the country to the verge of starvation.
Tehran has repeatedly denied arming the rebels, which would violate a United Nations weapons embargo slapped on Yemen in 2015.
An overwhelming 75 percent of the population - 22 million people - is in need of aid, seven million of whom are at risk of starvation, while one million Yemenis have been ill from cholera.
Mark Lowcock, the UN's humanitarian chief, warned that unless additional steps are taken, Yemen faces the prospects of "another major" cholera outbreak after more than a million people fell ill a year ago.