House Speaker Paul Ryan plans to introduce legislation this week to suspend the U.S. refugee program amid political wrangling over the fate of Syrian migrants. The Wisconsin Republican earlier Tuesday joined some lawmakers and numerous state governors in calling for a halt on refugee settlement after the deadly terrorist attacks in Paris last week. Senate Majority Leader Mitch McConnell, R-Ky., also urged a suspension or stop of the refugee program Tuesday. On Monday, the State Department said it would not change its plan to accept 10,000 Syrian refugees in the next year amid ongoing conflict in the country. States do not have the authority to refuse entry to migrants because resettlement is federally funded. Many Democratic governors continue to support the refugee plan. Others, including Florida Gov. Rick Scott, have urged Congress to take action.

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In the days since the attacks, Republican governors of about 30 states expressed reservations about new settlement of migrants, citing security concerns. One Democrat — Gov. Maggie Hassan of New Hampshire — urged the federal government to stop admitting refugees until more is known about its vetting process.

Europe's migrant policy has been in focus after it emerged that a suspected attacker may have entered the bloc through Greece. Some European policymakers have urged restraint on a tough response.

The White House plans to hold a conference call with governors later Tuesday, according to Reuters, citing media reports. It was not immediately clear how many states would participate. The Senate's top Democrat, Harry Reid of Nevada, said Tuesday that he expects the White House will say more on refugee policy soon.

President Barack Obama addressed the refugee plan at the G-20 meeting in Turkey on Monday. He called suggestions from political leaders that a religious test be applied to refugees seeking asylum in the U.S., "shameful."

"That's not American," he said. "That's not who we are. We do not have religious tests to our compassion." Read MoreObama to GOP: This is not a war on Islam