Mr Griffiths held several rounds of talks last week in Sanaa without being able to convince the Houthis to hand control over of the Al Hodeidah port to UN-supervised global forces.
Two civilians were killed in a shelling, carried out on Saturday by Yemen's Houthi militants on the Saudi southwestern city of Jazan, the Saudi Al-Ekhbariya TV channel reported citing Saudi-led Arab coalition's statement.
He said past and present United Nations efforts had been met with "intransigence" by the Houthis who he said have refused a political solution to end the crisis.
The United Nations pulled all of its worldwide staff out of Hodeida early Monday morning.
Al-Maliki said residents have welcomed the advancing government forces through such gestures like removing sectarian graffiti from walls of liberated towns and cities in Saada as well as the port of Hodeidah.More news: First ‘Bond girl’ Eunice Gayson dies aged 90
The U.N. considers Yemen to be the world's worst humanitarian crisis, with more than 22.2 million people in need of assistance.
Around 70 per cent of Yemen's imports, including the vast majority of its food, comes through Hodeidah and the port is described as the country's "lifeline".
Following the closed-door meeting, Russian Ambassador Vassily Nebenzia, who is council president this month, called for de-escalation and said the top United Nations body would be "closely" following developments. "It is essential for him to be given the time that he needs to facilitate a negotiated solution that avoids conflict in the city and we support his efforts to do so".
The council did not specifically call on the coalition to refrain from attacking Hodeida and diplomats said there had been much discussion over the president's statement to the press.
The UN has warned the Saudi-led coalition that a military attack or siege on the city, long a target in the war, could lead to the displacement of 250,000 people.
Meanwhile, US secretary of state Mike Pompeo said the US "is closely following developments" and has "spoken with Emirati leaders and made clear our desire to address their security concerns while preserving the free flow of humanitarian aid and life-saving commercial imports".More news: Singapore summit: Will striking a deal with Trump risk Kim's regime?
Griffiths is set to present on June 18 a new peace plan for Yemen, but he has warned that military action could derail that effort.
UN Secretary-General Antonio Guterres met with Yemen's foreign minister at UN headquarters amid warnings that an attack on Al Hodeidah was imminent.
"If an attack does take place, casualties on all sides will be high with a likely catastrophic impact on the civilian population", they wrote.
The three-year stalemated war has killed more than 10,000 people and displaced more than three million.
Since the Coalition launched its support for the Yemeni government in March 2015, Houthis have fired 149 ballistic issiles and 66,315 projectiles toward Saudi Arabia.More news: How to Customize What Gmail’s Swipe Gestures Do