AUSTIN, Tex. — Just over a week ago, white envelopes marked “URGENT REPLY ASAP” began arriving in the mailboxes of Texas Muslim leaders. Those who looked inside found an unusual document that turned out to be a highly inflammatory three-question survey investigating their views on elements of Islamic extremism.

The sender, as noted in the return address, was State Representative Kyle Biedermann, a central Texas hardware store owner who had officially become a member of the Legislature less than a month earlier. More than 400 surveys went out. Only one came back, Mr. Biedermann said.

The surveys were distributed as part of a campaign that Mr. Biedermann, a Republican, said was designed to expose “radical Islamic terrorism in Texas” and preceded a forum that Mr. Biedermann held on Thursday at the State Capitol to amplify that theme. But angry and insulted members of the Texas Muslim community, including prominent imams, are responding in a fierce pushback that included news conferences and at least one full-page newspaper ad.

The uproar in Texas came as President Trump, who as a candidate at times called for a ban on Muslim immigration to the United States, is preparing to roll out immigration policies that could include sharp restrictions on immigration from predominantly Muslim countries.

Muslim leaders said Mr. Biedermann’s surveys threatened to further escalate a rising pattern of intolerance toward Muslims with the approach of Texas Muslim Capitol Day on Tuesday, in which Texas Muslims visit the Capitol and meet lawmakers. Former State Representative Lon Burnam of Fort Worth, who sponsored the creation of the biennial pro-Muslim observance in 2003, described Mr. Biedermann’s actions as “nonsense, xenophobic.”

“His treatment of Muslims is giving fuel to the fire of Islamophobia that is running rampant in our state,” said Sarwat Husain, founding president of the San Antonio chapter of the Council on American-Islamic Relations and a national board member of the group. Speaking at a multifaith news conference at the State Capitol at the same time Mr. Biedermann was conducting his hearing two floors below, Ms. Husain said the letter was reminiscent of McCarthyism, calling it “very misleading, humiliating, intimidating, disgusting and downright offensive.”

The survey, and the meeting on Thursday, were aimed at sounding out Texas Muslims about…