Before leaving, Saleh asked his countrymen for forgiveness in a television address and said he planned to return home after surgery, in time for the swearing in of a presidential successor next month.
He has formally relinquished power to his vice president in anticipation of a presidential election Feb. 21.
The White House has been considering Saleh’s request since December, and a decision to allow him into the United States could be politically risky for President Obama, given Saleh’s repressive 33-year reign and the sustained unrest in Yemen.
Many Yemenis want Saleh to face trial for the deaths of hundreds of political dissidents over the years, but Yemen’s parliament reportedly approved immunity for him on Saturday.
On Sunday, the State Department said in a statement that “the sole purpose of this travel is for medical treatment and we expect that he will stay for a limited time that corresponds to the duration of this treatment.”
But Saleh suggested last month that the reason for him to come to the United States was to remove him from Yemen to help ensure a peaceful and orderly transfer of power. Demonstrators began demanding his removal from authority a year ago.
Saleh suffered serious wounds in a June attack on the palace, but he said last month that he would go to the United States “not for medical treatment, because I’m fine, but to get away from attention, cameras, and allow the unity government to prepare properly for elections.”
In Sanaa on Sunday, Abdul Hafeeth al-Nihari, the deputy chief of the media department of Yemen’s ruling party, described Saleh’s trip to Oman as “a brotherly visit” to improve the relationship between the two countries.
He stressed that Saleh would return to Yemen after his treatment in the United States.
“He will be back prior to the elections to hand over the presidency, and the presidential palace to his successor,” said Nihari. “He will back to practice his political life as the leader of the General People’s Congress,” Saleh’s ruling party.
Staff writer Sudarsan Raghavan in Nairobi and special correspondent Ali Almujahed in Sanaa contributed to this report.