Saudi Crown Prince Mohammed bin Salman and US national security adviser Jake Sullivan discussed the situation in Iran and steps aimed at ending the war in Yemen in a phone call on Tuesday.
"Mr Sullivan highlighted the remarkable progress in Yemen over the past year, during which fighting has nearly ceased under a UN-mediated truce," the White House said in a statement.
"He welcomed Saudi Arabia’s extraordinary efforts to pursue a more comprehensive road map for ending the war and offered full US support for those efforts."
The two sides also discussed a number of regional issues, including Washington's “unwavering commitment to ensure Iran can never acquire a nuclear weapon”.
They agreed to continue discussions around other important initiatives, such as the Global Infrastructure and Investment partnership, clean energy co-operation and investment in 5G and 6G Open Radio Access Network technology.
The call came amid talks in Yemen between Saudi Arabia, Oman and the Houthis in Sanaa, which began at the weekend.
US special envoy to Yemen Tim Lenderking is also scheduled to travel to the Gulf on Thursday, the White House said.
Mr Lenderking's visit to the region begins with the start of a three-day prisoner swap between the warring sides that will see 877 detainees being handed over.
As part of the exchange, an International Committee of the Red Cross flight from Sanaa to Riyadh will return more than 20 Saudi citizens to their country.
The swap was originally scheduled for Tuesday, but was later moved to Friday and then back to Thursday due to logistical reasons.
“On the first day of the exchange [Thursday], ICRC flights will transport detainees between Aden and Sanaa,” Yemen's Deputy Human Rights Minister Majed Fadhil, who is part of the negotiation committee, told The National on Tuesday.
Friday will see flights from Sanaa to Riyadh, Abhaa to Sanaa, and both ways between Mokha and Sanaa, while Saturday will see flights both ways between Marib and Sanaa, he added.
On Tuesday, Prince Mohammed and American Senator Lindsey Graham also discussed the kingdom's continuing reforms and trade between Saudi Arabia and the US trade during a meeting in Jeddah.
Saudi Arabia announced a deal worth up to $37 billion last month in which its two national airlines will order as many as 121 commercial jets from US aircraft maker Boeing.
“I look forward to working with the administration and congressional Republicans and Democrats to see if we can take the US-Saudi relationship to the next level, which would be a tremendous economic benefit to both countries and bring much-needed stability to a troubled region,” Mr Graham said.
Last week, CIA director William Burns met the kingdom's intelligence officials in Riyadh.
Yemen is in its eighth year of war since the Iran-backed Houthis took over the capital Sanaa in 2014, prompting the government to request assistance from Saudi Arabia to restore it to power.
Yemen's Foreign Minister Ahmad Awad bin Mubarak and analysts believe that Saudi Arabia's rapprochement with Iran last month gave political peace in Yemen a "positive momentum" and made reaching a deal with the Houthis more likely to happen, especially since talks over a prisoner swap had been stalled for at least three years.
