The state Assembly’s Democratic majority, citing criticism from the US surgeon general, will demand this week that recently cut anti-smoking funding be restored, said a legislative official familiar with the issue.

The budget proposal the Assembly is to make public tomorrow will include “partial restoration” of funds for smoking-cessation programs aimed primarily at teenagers, the official said.

Gov. Cuomo wants to slash $5 million of the program’s $41 million, which is half of what it was in 2008.

The Centers for Disease Control said New York, based on its population, should spend $254 million on the initiative.