Bee Moorhead, executive director of Texas Impact, a statewide religious advocacy network that includes Christians, Jews and Muslims, said the group sent a letter to mosques and Muslim organizations urging them to disregard the survey. “What’s wrong with it is that an elected official in a position of power sent out that letter in a way that would have made someone think the survey was an official piece of business of the State of Texas,” Ms. Moorhead said in an interview. “It was an intimidating and misleading piece of communication on the part of a public servant.”

Mr. Biedermann, who was sworn in when the Legislature convened on Jan. 10, said the House leadership approved his use of a committee chamber to conduct his hearing, but the House speaker, Joe Straus, signaled his disapproval. “I believe it is wrong and offensive to single out any group based on their religion,” Mr. Straus, a San Antonio Republican, said in a statement released by his office.

Muslim leaders and supporters from other faiths said on Thursday that intolerance against Muslims has been on the rise both nationally and in Texas. As a Texas senator in 2007, Lt. Gov. Dan Patrick boycotted the first Muslim prayer delivered in the Texas Senate, saying he did not want his presence in the chamber to “appear that I was endorsing that.” Armed protesters have also appeared outside mosques in the Dallas-Fort Worth area.

In 2015, State Representative Molly White, a Republican from Belton in central Texas, ignited a firestorm by demanding that Muslims in town for that year’s Muslim Day publicly declare their allegiance to the United States before entering her office.

Mr. Biedermann said his efforts were designed to increase public awareness about what he called an expanding threat in the form of Islamic terrorism that, he said, is spreading into the United States from across the southern border. In opening his hearing, he said that many crossing the border illegally came from countries with ties to terrorism, such as Iraq, Iran, Syria, Afghanistan and Pakistan. “With the rise of radical Islamic terrorism at home and throughout the world, homeland security must be our top priority,” he said.

In an interview afterward, Mr. Biedermann said border security and the threat of terrorism were cited as the “No. 1 issue” by thousands of voters in his district when he was campaigning for the legislative seat, which he won in a runoff. He says his office is open to “Texans of all backgrounds and religions.”

Mustafa Tameez, a Muslim who was a consultant to the Department of Homeland Security in the Bush administration, said the survey was “a roundabout way of trying to get people to sign some kind of loyalty pledge, and that’s not where the threat is coming from.”

“The people that are the real threat are individuals who have self-radicalized or radicalized over the internet,” Mr. Tameez said.