Iran-backed Houthis have been battling the government, which is supported by Gulf states.
US Secretary of State John Kerry said: "We cannot emphasise enough today the urgency of ending the violence in Yemen."
He made the statement after meeting British foreign minister, Boris Johnson, and other officials in London.
ITV News has been reporting on the dire humanitarian situation unfolding in Yemen.
The attack was one of the deadliest in the country's civil war and has been blamed on the Saudi-led coalition.
ITV News witnessed the aftermath of the attack and was shown remnants of a bomb, which a Yemeni military official has claimed came from a US-made Mark 82.
Kerry said he, Johnson and Cheikh Ahmed were calling for theimplementation of the ceasefire "as rapidly as possible, meaningMonday, Tuesday".
Kerry said if Yemen's opposing sides accepted and moved forward on the ceasefire then the special envoy to the UN, Ould Cheikh Ahmed, would work through the details and announce when and how it would take effect.
"This is the time to implement a ceasefire unconditionally and then move to the negotiating table," Kerry added.