Earlier, medics said at least 20 people were killed when coalition warplanes bombed two buildings in the capital Sanaa, which the rebels overran a year ago.
While in Aden, Hadi will inspect damage caused by the fighting, the statement said.
The pre-dawn air walkouts on Sanaa targeted Saleh’s followers as well as the Shiite Huthi rebels, witnesses said.
A regional official in Marib said on Monday that the battlefronts had been quiet since the Arab coalition spearheaded by UAE forces completed “securing” the environs of Marib city.
Monday was declared a “public holiday” across northern Yemen, as the Shi’ite Houthi movement commemorated the one-year anniversary of capturing the capital city of Sanaa away from the previous government.
One of the freed Americans was identified as Scott Darden, a 45-year-old employee of the New Orleans-based company Transoceanic Development, who was taken hostage by Houthi rebels in Sanaa in March, the USA administration official said.
A former army general and vice president, Hadi assumed office in 2012 under a Gulf-brokered transition plan following “Arab Spring” protests which ended over three decades of rule by his predecessor, Ali Abdullah Saleh.
More than 21 million people – over 80 percent of Yemen’s population – are in urgent need of aid, and some 9.4 million Yemenis have problems accessing water, according to the UN.
The stalled advance has prompted Hadi to call the Marib governor and a local military commander, according to Yemeni presidential officials, who like the security officials interviewed by the AP spoke on condition of anonymity because they were not authorized to talk to reporters about battlefield strategies.
But as Prime Minister Khaled Bahah returned from exile to the main southern city of Aden last week, he acknowledged that his government still faces challenges, even in the south.
Such cross-border shelling has been common since a Saudi-led coalition began a campaign of airstrikes in March against Yemen’s Shiite rebels, known as Houthis.
Worldwide human rights groups have voiced concern at the growing number of civilians killed in the intensifying air war.
Scores of civilians including children have been killed in heavy Saudi-led airstrikes in recent weeks as organizations repeated calls for independent investigations into indiscriminate attacks by the warring parties in the country.
The spokesman did not say when or where inside Yemen the incident took place.