The governor’s office did not respond to multiple requests to specify what services Mr. Christie intended to withhold.

In a statement on Monday, Brian Murray, the governor’s spokesman, said that “in this case and all prior, the federal government has failed to consult with New Jersey, has shared no security or background information and can give no assurances about the integrity of the resettlement process.

“Rather than address concerns expressed by governors of both parties and the director of the F.B.I., the federal government has chosen instead to persist with its plan to increase the number of new refugees at a previously unattainable rate. Governor Christie will remain opposed to the continuation of this program until the fundamental concerns for our national and state security are addressed.”

Mr. Christie was one of 30 state governors who said the refugees were not welcome in their states.

Mr. Obama said the United States would accept at least 10,000 Syrian refugees this year. The State Department said it had no plans to curtail its programs, which have put refugees in 180 communities across the country. Officials with Church World Service, one of the nine national resettlement groups contracted by the federal government and the one that resettled the family on Monday, said it was proceeding as scheduled.