Chen Guangcheng, the blind Chinese activist who sought refuge in the US embassy in Beijing, is staying in China after authorities promised he would be safe, US officials have said.

Hillary Clinton, the US secretary of state, who arrived in the Chinese capital on Wednesday morning, said it was crucial to make sure those pledges were kept.

The "barefoot lawyer", who made a remarkable escape from a punishing 19-month regime of extralegal house arrest last week, was reunited with his wife and children as he underwent medical checks at a Beijing hospital. Speaking via a lawyer, the 40-year-old said he had received "clear assurances".

China has demanded that the US apologise for taking him into the embassy in "an irregular manner".

"The US method was interference in Chinese domestic affairs, and this is totally unacceptable to China. China demands that the United States apologise over this, thoroughly investigate this incident, punish those who are responsible, and give assurances that such incidents will not recur," the foreign ministry spokesman Liu Weimin added in a statement carried by Xinhua. The state news agency said Chen had spent six days at the embassy and left "of his own volition".

But Clinton said her country had handled the case "in a way reflecting his choices and American values". The US secretary of state, who is in China for scheduled bilateral talks that have been overshadowed by Chen's case, said China had promised he could pursue a university education in a safe environment.

"The United States government and the American people are committed to remaining engaged with Mr Chen and his family in the days, weeks, and years ahead," she said.

In a phone call made on his way to hospital, Chen thanked Clinton for her support and told her: "I want to kiss you", US officials said.

Chen is being treated in the VIP clinic on the ninth floor of Chaoyang hospital, on the east side of the city.

His wife, Yuan Weijing, who was waiting there with their exhausted 10-year-old son and six-year-old daughter, told the Guardian: "I'm OK. We don't know yet [what's wrong with him]. He's having a check-up."

She said they had arrived in Beijing on Wednesday. Supporters had been gravely concerned for the safety of the family, particularly because Yuan had previously been badly beaten by their guards in Dongshigu.

The US ambassador, Gary Locke, and the state department legal adviser Harold Koh accompanied him to the hospital.

US officials speaking on condition of anonymity said staff had helped Chen enter the mission because he needed medical care following his escape.

"This was an extraordinary case involving exceptional circumstances, and we do not anticipate that it will be repeated," one said.

He did not elaborate and it is not clear exactly how Chen entered. But while the activist had apparently hoped to stay in safe houses in Beijing, friends concluded that he could not be protected unless he went to the US embassy and discussed asking for a car with diplomatic number plates to pick him up.

The official also said Chen had not asked for asylum, although in any case it cannot be granted to people outside the US.

But concern remains about Chen's future. In the past both he and his wife have been abducted from the capital by local officials.

The lawyer Teng Biao, a friend and supporter of Chen, tweeted: "Guangcheng and Weijing met in Beijing and didn't have to worry about being kidnapped. Congratulations! This is the first time."

Wang Songlian, of the Chinese Human Rights Defenders network, warned: "If he's going to stay in China, reassurances are not very reassuring because the Chinese government has a record of not honouring its words regarding human rights."

"The most worrying part is that his extended family is in Shandong and authorities could retaliate by detaining or torturing them. We know four are in custody and one [his nephew, Chen Kegui] is accused of injuring government officials."

She gave short shrift to the Chinese demand that the US say sorry over Chen's case.

"I think it's incredible that the Chinese government would ask for an apology from the US when it has unlawfully put a human rights activist and his family under house arrest for so long," Wang said.

Chen's case has been regarded as one of the most egregious cases of official abuses. The self-taught legal activist was initially praised by authorities for using his skills to help disabled people and farmers with problems. But he angered officials in Linyi city, eastern Shandong province, after attempting to help women forced to have abortions and sterilisations. He was jailed for more than four years on what supporters described as fabricated charges and placed under a brutal regime of house arrest on his release in 2010.

One Chinese Twitter user, @jianzhang1984, wrote: "For a blind person, China sent 100 hooligans and several spokespeople from the foreign ministry. The US sent one ambassador, one assistant secretary of state and one top lawyer … It is very clear to see which is a hooligan country and which country is a world leading country."