This came in a post Al-Mekhlafi published on his Twitter account on Wednesday.
Al-Mekhlafi posted: "In Yemen, legitimacy has agreed to a ceasefire, but the Houthis have continued to fight and kill everywhere."
In the same tweet, the presidential advisor and former foreign minister called on the UN envoy to admit his failure and to resign because: "He did not convince Al-Houthi to cease the fire under these circumstances."
According to Al-Mekhlafi: "Because of the coronavirus pandemic that threatens humanity, all the countries at war have declared a ceasefire."
The Yemeni government and the Houthi group have previously welcomed United Nations Secretary-General Antonio Guterres's request to end the fighting in the country.
At the end of March, Guterres called on the: "Warring parties in Yemen to cease hostilities and do their best to counter the coronavirus outbreak."
The fronts of the fighting in the governorates of Al-Jawf and Ma'rib (north and east) are witnessing an escalation of tension between government forces and the Houthi fighters, in spite of announcing the approval of the ceasefire.
For the sixth year in a row, Yemen has been witnessing a war between pro-government forces and Houthi militants accused of receiving Iranian support and controlling governorates, including Sanaa, since September 2014.
Since March 2015, a Saudi-led Arab military alliance has been supporting government forces against the Houthis, in a war that resulted in "the worst humanitarian crisis worldwide", according to the United Nations.