WASHINGTON — Seizing on the terrorist attacks in Paris, congressional Republicans on Tuesday demanded the suspension of a program to accept Syrian refugees in the United States, but along with Democrats, they continued to shy away from explicit authorization of military force to confront the Islamic State.

Speaker Paul D. Ryan of Wisconsin was the leading voice in his party urging an immediate halt to the refugee program. More than two dozen Republican governors are pledging to try to block the entry of Syrian refugees, and all the Republican presidential candidates have called for barring the refugees entirely or limiting the group to Christians.

President Obama, on a trip to Manila, expressed outrage at what he called “political posturing” by Republicans on the issue, accusing them of making statements that the Islamic State could use as a recruiting tool.

“When candidates say we should not admit 3-year-old orphans, that’s political posturing,” the president said. “When individuals say we should have religious tests, and only Christians, proven Christians, should be allowed, that’s offensive and contrary to American values.”