During his trip, Mr Lenderking “will meet Yemeni, Saudi, Emirati, Omani and international partners to discuss the necessary steps to secure a durable ceasefire and launch an inclusive, UN-mediated political process while ensuring continued efforts to ease the economic crisis and suffering of Yemenis”, the department said in statement.
The truce “has delivered the longest period of calm since the war began”, helping Yemenis “to shape a brighter future for their country”, the department added.
The UN helped to mediate a truce last year between Yemen and the Iran-backed Houthi rebels, ending much of the fighting.
The men were seized in Abyan province 18 months ago by Al Qaeda in the Arabian Peninsula.
The visit also comes a week after most of the 1.14 million barrels of oil aboard the ageing FSO Safer was offloaded last week. The oil on the disintegrating tanker had threatened to cause an environmental disaster for years.
An international crew had pumped the oil aboard the FSO Safer on to the Nautica in a transfer that began on July 25. The UN said less than 2 per cent of the original oil remains mixed with sediment, which will be removed during the final cleaning.
The operation to transfer the oil and tow the FSO Safer was expected to cost $143 million. There remains a $22 million funding gap to tow the ship to a scrapyard.
Mr Lenderking will work with donors to help raise the $22 million and “address all residual environment threats”, the State Department said.
During his trip to the Gulf, he will also congratulate Yemeni, UN and international partners on the offloading of the barrels from the tanker.