JERUSALEM — The State Department sent a message to Gaza’s Hamas leaders on Thursday that it would withdraw some $100 million it is spending in Gaza on health care, agriculture and water infrastructure if they did not back off a demand to audit the books of American-financed charities operating there.

The threat, delivered via an intermediary, came after Hamas officials suspended the operation of the International Medical Corps on Sunday for its refusal to submit to a Hamas audit at the charity’s site.

Tensions have been simmering for months over Hamas’s relations with the nongovernmental organizations of a number of countries operating in Gaza as the authorities have sought to increase surveillance of the groups. Early this year, Hamas asked all such groups to register with the central government, pay a fee and submit financial reports.

Although those requests were resisted, most groups ultimately agreed to them, officials at charities based in Gaza said. But in June, when Hamas demanded that the groups permit its officials to audit their books, the objections grew. Though Hamas did not explain the reason for its demand, many governments are suspicious of foreign financing of charities, fearing that money can be diverted for political or intelligence-gathering uses.

For American organizations, United States policy forbids direct contact with Hamas, labeled a terrorist group by the State Department. As a result, on-site audits by Hamas officials would lead to suspension of aid, American officials said. The United States accounts for a large share of the money that foreign governments spend on humanitarian assistance in Gaza.

The hope of the charities and American and European officials is that Hamas will drop its demand in the coming days so that all programs can continue. They argued that the insistence on on-site audits violated Palestinian law and American policy. All officials spoke on the condition of anonymity because negotiations with Hamas were continuing.

But Taher al-Nounou, a spokesman for the Hamas government, rejected their argument, saying: “These organizations do not recognize and do not want to recognize the Palestinian law. We do not kneel down to any threat. Any organization that wants to operate in the Palestinian territories must respect the laws.”

Aid provided by American and other foreign groups goes to hundreds of thousands of Palestinians in Gaza, where most of the 1.6 million residents are refugees. Like the Palestinian Authority in the West Bank, Hamas has had trouble meeting its payroll recently, and foreign officials hope that the threat of losing outside financing will persuade Hamas officials to drop their demand.

There may be disagreement among various ministries and officials, with some insisting on the audit and others willing to abandon it.

American and some other foreign governments do not consider Hamas the legitimate government in Gaza. Although Hamas won Palestinian parliamentary elections in 2006, the Palestinian Authority, dominated by Fatah, is still viewed by many abroad as the legitimate government in Gaza and the West Bank.

The authority was thrown out of Gaza in 2007 after a brief civil war and now governs only in the West Bank. Hamas set up its own government in Gaza after that. Relations between Hamas and Fatah have alternated between tense and vicious, although the two factions are now trying to negotiate a reconciliation.

Most foreign charities submit their own audits to the Interior Ministry in Ramallah in the West Bank, under their interpretation of Palestinian law. They also publish reports on their sources and activities and believe that should suffice for Hamas.

In July Norway’s government sent Hamas a letter saying it was “clear under Palestinian law that the competent authority to monitor the activities of the NGOs is the P.A. Ministry of Interior in Ramallah.” If Hamas insisted on an on-site audit, the organizations “might suspend their operations, which will affect significant parts of Gaza’s population who depend on outside assistance.” It said the Norwegian government would hold Hamas responsible for the suspension in services.