Dozens of mostly Republican governors are vowing to block President Barack Obama's plan to accept 10,000 Syrian refugees into the U.S. But on Tuesday, Governor Andrew Cuomo questioned their authority to opt out. Washington bureau reporter Geoff Bennett filed the following report from the White House.

More than half of the nation's governors say Syrian refugees are not welcome in their states.

"Until we are thoroughly satisfied of the federal background checks conducted on such refugees entering our country," said North Carolina Governor Pat McCrory during a Monday news conference.

The governors oppose President Barack Obama's plan to relocate 10,000 Syrians who are fleeing their country's civil war. Authorities say at least one of the suspects believed to be involved in the Paris terrorist attacks came through Europe posing as a refugee from Syria.

Immigration, though, is a federal matter. Governors don't have the legal standing to reject refugees, which Governor Andrew Cuomo pointed out Tuesday, while speaking at Harvard University.

"The governors who say, 'I will refuse to let the refugees in.' How? How?" Cuomo said.

The mostly Republican governors who are raising concerns say they want assurances about the government’s refugee vetting process.

"We need to hear from the White House and DHS on exactly what these background checks are," McCrory said in an interview with CNN.

A senior Obama administration official says the screenings are rigorous.

"This is the most stringent and thorough vetting process for anyone trying to get into the United States," said White House Communications Director Jen Psaki.

Before a refugee ever steps foot on American soil, personal information is checked against a number of federal and international databases. The process can take years to complete.

On Tuesday, Mayor Bill de Blasio issued a statement of support for allowing refugees to enter the U.S., saying in part, "New York City is a proud immigrant city, and we will not turn our back on that history or the people being persecuted and fleeing war."

The Obama administration agrees.

"We should not change who we are out of fear or lack of information about how the process actually works," Psaki said.

Despite the growing number of Republicans who want to stop the president's plan to accept thousands of Syrian refugees, the Obama administration says the president has no intentions of slowing or stopping that process.