The war has killed more than 10,000 people and created the world's worst humanitarian crisis, with disease and hunger rife.
"We are putting teeth behind these demands with regular oversight, sanctions and suspension of weapons sales and refueling support", Menendez said.
The US Senate on Thursday introduced a legislation seeking to punish Saudi Arabia over the killing of Saudi journalist Jamal Khashoggi and escalating the political as well as a humanitarian crisis in Yemen.
The UN official also told reporters about a harrowing testimony provided by a doctor at the hospital who said that "every day about 50 children are brought to us", adding, "We have to send 30 home to die".
"This is a crucial moment for Yemen", he said, warning that a flare-up of fighting on the ground could derail the peace effort. "I believe we are close to resolving issues to make this happen".
The conflict in Yemen began with the 2014 takeover of the capital of Sanaa by the Iranian-backed Houthis, which toppled the government of Abed Rabbo Mansour Hadi.
Oddly, Saudi coalition spokesman Col. Amnesty International has documented serious threats to the hundreds of thousands of civilians believed to remain in the city, unable to leave due to the currency collapse, vastly increased fuel prices and exorbitant rents elsewhere. The Houthis have fired long-range missiles into Saudi Arabia and targeted vessels in the Red Sea. "A new worry is that employees at the port say the Houthis have started mining all of the entrances except one".
Martin Griffiths told the UN Security Council on Friday that the Yemeni government and Houthi rebels had shown a "renewed commitment" to work on a political solution to end a war that has driven millions to the brink of starvation. "I will also be happy to travel myself, if necessary, with the delegation to the consultations", Griffiths said. "Both are going to be required to avert a starvation", he said.
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The situation has worsened over the previous year as the economy has collapsed and the currency has sharply declined in value.
Griffiths said this week's sudden halt in an offensive by Saudi-led forces to try to recapture the city of Hudaydah was an important condition for a resumption of dialogue.
"In room after room after room, you see these little children dying before your very own eyes", Beasley said. He vowed: "Let us build on this rather than retreat from this".
United Nations humanitarian chief Mark Lowcock urged the Security Council to help avert a catastrophic deterioration of the situation.
The port of Hodeidah functions as a lifeline for humanitarian aid to over 14 million Yemenis, acting as an entry point for 80 percent of Yemen's food and supplies.
Britain's United Nations ambassador, Karen Pierce, said she will circulate a Security Council resolution Monday to address the Yemen crisis and put Lowcock's requests "into practice".
"This war must end soon and it won't end on the battlefield", US Deputy Ambassador Jonathan Cohen told the council, renewing a US call for a cessation of hostilities and talks.
"I'm not asking that we end our alliance", Paul said.