Yemeni President Ali Abdullah Saleh, pictured in December.

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NEW: Protesters continue demonstrations in Yemen's capital

Yemeni government sources say President Ali Abdullah Saleh left Oman Monday

He is scheduled to return to Yemen in February, the embassy says

The State Department says Saleh can come to the U.S. for medical treatment

Sanaa, Yemen CNN  — 

Yemen’s embattled president was on his way to the United States for medical treatment Monday, officials said.

President Ali Abdullah Saleh left Yemen on Sunday and stopped in Oman before continuing Monday on a trip to the United States, Yemeni government sources said.

The purpose of Saleh’s U.S. trip is a “private medical visit,” the Yemeni Embassy in Washington said in a statement Sunday.

“The president will travel back to Yemen in February to attend the swearing-in ceremony of the newly elected president,” the statement said.

At least six family members were with Saleh, two senior Yemeni government officials said.

Saleh was wounded in a June bomb attack on his presidential palace.

His request to travel to the United States has been approved, the U.S. State Department said Sunday.

“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 became the fourth Arab leader forced from power last year when he signed a Gulf Cooperation Council power transfer deal aimed at ending his country’s months-long political crisis.

On Saturday, lawmakers in Yemen approved a controversial law giving Saleh immunity from prosecution – a key element of the November deal.

In return, Saleh will step down from power in Yemen next month after ruling the country for more than 33 years.

Although the deal was hailed by opposition parties in Yemen, youth protesters and international rights groups called the immunity a violation of international law.

Protesters have demonstrated for months in Yemen, calling for Saleh to step down.

Saleh apologized to his people and called for protesters to stop demonstrations in a speech broadcast on Yemeni state television before his departure Sunday.

“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.

But word that Saleh had left the country did not quell protesters’ criticisms there.

Protesters set up tents in Sanaa Monday, repeating anti-Saleh chants for hours.

Organizers said protests against Saleh and his ruling family would continue for months – just as they did when the president was in Saudi Arabia for treatment after the June attack.

“Saleh left (for) Saudi months ago, but came back. It’s not over for Saleh,” said Hussein Mansoor, a protester in Sanaa. “We want him to come back to Yemen so that he is tried for his crimes.”

Mansoor said that Saleh does not deserve immunity and must be held accountable.

“Saleh will end up like (former Tunisian President Zine el Abidine) Ben Ali, (former Egyptian President Hosni) Mubarak, or (former Libyan leader Moammar) Ghadafi. There is no fourth option,” he said.

Journalist Hakim Almasmari reported from Sanaa. CNN’s Mohammed Jamjoom reported from Abu Dhabi.