Sanaa, Yemen (CNN) -- Embattled Yemeni President Ali Abdullah Saleh was en route to the United States for medical treatment Sunday, officials said.
Saleh arrived in Oman earlier and was on his way to America, Vice President Abdurabu Hadi said.
"The president will travel back to Yemen in February to attend the swearing-in ceremony of the newly elected president," the Yemeni Embassy in Washington said. The purpose of his U.S. trip is a "private medical visit," it added.
At least six family members were with Saleh, two senior Yemeni government officials said.
Yemeni state television reported earlier Sunday that Saleh had announced he was going to the United States for treatment.
Saleh was wounded in a June bomb attack on his presidential palace.
The U.S. State Department said Sunday that his request to travel to the United States had been approved.
"As we have indicated, 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," the department said in a statement.
Saleh's departure came a day after Yemen's parliament approved a controversial law giving the president complete immunity from prosecution. In return, Saleh will step down from power in Yemen next month after ruling the country for more than 33 years.
Protesters have demonstrated for months in Yemen, calling for Saleh to step down.
In a speech broadcast on Yemeni state television Sunday, Saleh apologized to his people.
"I ask for forgiveness from my fellow citizens, men and women, for any negligence during my presidential term in the last 33 years, I ask for forgiveness and I apologize to all Yemeni citizens," he said.
He called for protesters to stop demonstrations.
"Young men, go back to your homes, go to your families. I feel sorry for you, I call on you to go back to your homes and start a new page with the new leadership," he said.
Word that Saleh was leaving the country did not quell protesters' criticisms there.
"If Saleh thinks that because he left the country we will head back home then he is wrong. We left our homes demanding complete change and will not go back until we reach our goal. The Yemeni revolution is for real," said Saba al-Shibami, a youth activist in Sanaa.
She was among thousands of protesters in Sanaa's Change Square vowing to continue demonstrations until Saleh is prosecuted for alleged human rights violations, including the deaths of protesters. Demonstrations in 14 Yemeni provinces Sunday protested the immunity deal, activists said.
The immunity law was a key element in the Gulf Cooperation Council power transfer deal Saleh signed in November.
Though the deal was hailed by opposition parties in Yemen, youth protesters and international rights groups called the immunity a violation of international law.
Protesters Sunday chanted "No immunity will save you. Justice will prevail" and "Saleh, Saleh, wait and see, your future will be painful."
Demonstrators also criticized opposition leaders, claiming that they had sold out the country.
"Who are they to grant Saleh immunity? The opposition are not the ones who lost loved ones. They have no authority to grant a killer immunity," said Ali Shajerah, a youth activist in Sanaa.
Opposition parties defended their stance, saying it was necessary and for the best of interest of Yemen.
"The immunity was important and it makes Yemen a safer country. Let us help Vice President Abdurabu Hadi build this nation," said Mohammed Abulahoum, the president of the opposition Justice and Building party.
He said a revolution was continuing in Yemen.
"Yemen needs a new direction and for this to happen, Saleh had to leave."
Saleh said he would return to Sanaa as the president of his party, the General People's Congress, according to state television.
Senior ruling party officials said that Saleh would be back in less than a month to support Hadi's presidential nomination.
"When Obama leaves the U.S., Americans do not say that he will not be back. The same thing with President Saleh. He will be back to Yemen and will lead the General People's Congress party," said Mohammed Shaef, a senior GPC official and tribal chief of Bakeel, the country's largest tribe.
CNN's Yousuf Basil and Shirley Henry contributed to this report. Journalist Hakim Almasmari reported from Sanaa. CNN's Mohammed Jamjoom reported from Abu Dhabi.