Mohamed Al Jaber said his effort was to end the crisis in Yemen and support the 2021 Saudi Initiative to reach a comprehensive political solution in the country.
A deal would encompass a prisoner exchange, Mr Al Jaber said, confirming earlier reports of what the truce entails.
“The Kingdom’s Government and people have always stood with our brothers in Yemen during dire political and economic circumstances and crises,” he said on Twitter on Monday. “Since 2011, these brotherly efforts have continued to achieve the aspirations of the brotherly people of Yemen to restore security, stability and economic prosperity.”
The UN said it was not involved in the Omani, Saudi and Houthi talks in Sanaa.
A UN-brokered truce in Yemen ended last October despite major concessions from the Saudi-supported government which include the reopening of Sanaa international airport, six years after its closure.
More than 40,000 passengers have travelled to and from the Houthi-run capital since its reopening.
Earlier on Monday, UN Special Envoy to Yemen Hans Grundberg called the Saudi-Houthi talks, “the closest Yemen has been to real progress towards lasting peace”.
“This is a moment to be seized and built on and a real opportunity to start an inclusive political process under UN auspices to sustainably end the conflict,” Mr Grundberg told AP.
Ahead of the Saudi ambassador's trip to Sanaa, Saudi Arabia released 13 Houthi prisoners in exchange for a Saudi detainee.
Another prisoner exchange is set to take place on Friday, brokered by the International Committee of the Red Cross (ICRC) after being initially slated for April 11, Yemen's Deputy Human Rights Minister Majed Fadhil, who is part of the negotiations committee told The National.
The 887-person swap will include prominent Yemeni detainees to be released from the Houthi side.
They include Nasser Mansur Hadi, brother to Yemen's former president Abdrabbuh Mansur Hadi, former defence minister Mahmoud Al Subaihi, and Mohammad Abdullah Saleh, brother of Yemen's vice president Tareq Mohammad Abdullah Saleh.
The prisoners also include 23 Saudis and three Sudanese civilians, Hamed Ghalib of Yemen's National Resistance, which is involved in the negotiations with the Houthis, earlier told The National.
The detainees will first be transferred between Sanaa and Aden, then between Sanaa and Riyadh, and finally between Sanaa and Marib, he said.
“Talks between the Saudis and the Houthis never stopped even during the war, whether on political or security issues,” Yemen's Foreign Minister Ahmad Awad bin Mubarak told Cairo TV on Sunday.