The language subjecting the foreign groups to oversight by the police is likely to remain in the final version, according to a report by Global Times, a state-run newspaper. That would affect more than 7,000 groups operating in China.

Xinhua said one notable change in the new draft was a phrase giving examples of foreign groups that would be regulated by the law. The new draft says the law would apply to groups “such as foundations, social groups or think tanks,” the news agency reported. Exchanges with academic groups, schools and hospitals would be handled according to the “relevant provisions of national law.”

Critics of earlier drafts said those drafts were so broadly worded that any foreign university or educational group trying to work or hold activities in China would be subject to the new law and police oversight. The Xinhua report implied that might not be the case, but the wording was vague.

Jeremy L. Daum, a senior researcher at the China Center at Yale Law School, wrote on the China Law Translate blog on Monday that the wording used by Xinhua left “foreign and domestic organizations guessing what activities might be covered.”

Mr. Daum also said the new draft, as outlined by Xinhua, would allow the police even more powers over foreign nongovernmental organizations, beyond the earlier proposed abilities to search offices at any time, limit incoming funds, cancel activities and revoke registration. According to Xinhua, the current draft says the police have the authority to summon representatives to give them a “talking to.” Security officers have long been able to do that, but the law would make that authority explicit.

China has not previously had rules allowing for official registration of foreign nongovernmental organizations, forcing many to operate in a legal gray area here. Legal experts have said such rules should be put in place.

But the same experts have also said it makes no sense for oversight and registration of such groups to be given to the Ministry of Public Security. The Civil Affairs Ministry would be a more suitable institution, they say.