In a statement, Governor Hassan said U.S. intelligence and defense officials need to assure that the process for vetting refugees is "as strong as possible."
Until that happens, says Hassan, "the federal government should halt acceptance of refugees from Syria."
Senator Kelly Ayotte also says no refugees should be allowed into the country until the government can "100 percent guarantee" they are not affiliated with the Islamic State.
Senator Jeanne Shaheen, meanwhile, notes that the N.H. accepted 3 refugees from Syria last year, and says it would be wrong to halt the U.S's resettlement program.
"Its important for us to respond to this refugee crisis and make sure that refugees that are vetted can come to this country. That's our history -- we are an immigrant country --but its also a response to the challenge that Europe is facing, not just from ISIS and these terrorist attacks, but also from an overwhelming number of refugees."
President Obama has proposed the US take 10,000 Syrian refugees. In a news conference he promised rigorous screening and said it would be a betrayal of American values to "slam the door in their faces."