President Obama’s schedule this month epitomizes the complicated relationship he has with his most supportive group of religious voters: Muslims.

On Thursday, the president took to the podium before an annual D.C. gathering of Christians — the National Prayer Breakfast — and reminded the audience that Christians shouldn’t “get on their high horse” about the connection between the Islamic State and Islam. He noted the Crusades, the Inquisition and slavery — all undertaken “in the name of Christ.” The day before, Obama hosted an event that Muslim American leaders said was the first occasion in six years that a Muslim-only group has had a significant roundtable with the president.

Yet in two weeks, the White House is scheduled to host a key summit about violent extremism that is likely to focus on Muslim militants, an ongoing framework that angers many Muslim American leaders and is a thorn in their relationship with the president.

“A grave concern for many is that the government views us through a security lens and not through the broad role we play in American life and society,” said Farhana Khera, executive director of the civil rights group Muslim Advocates. “We thought it was crucial to have a sit-down meeting with the president about our hopes and dreams before they are potentially bringing in Muslims [at the Feb. 18 summit] to talk about extremism and violence.”

The hour-long meeting Wednesday afternoon included about a dozen leaders from across the spectrum, including Khera, prominent African American scholar Sherman Jackson, comedian Dean Obeidallah (who joked in a piece called “Muslims Infiltrate the White House! Me Included!” that he had pondered how to steal official plates and glasses) and Maya Berry of the Arab American Institute.

Several participants said the meeting stood out for its main topics — health care, racial profiling and employment — rather than extremism, which they said isn’t something the typical Muslim, even Muslim leaders, can do much about. Many Muslim Americans consider the link many make between their faith and extremism to be deeply prejudicial and want the president to speak more often about Muslims in other contexts.

“When you look at the number of terrorist incidents [in the United States] in the last 13 or 14 years, the vast majority have been perpetrated not by Muslims but by eco-terrorists and right-wing types. Our concern is with government programs seeking to address extremism that focus on American Muslims and that kind of skew the public’s mind and also skew how government resources are spent when there is a great diversity of threat facing our country,” said Khera.

“The Paris attacks and Boston Marathon attacks underscore that we need law enforcement focusing where they have legitimate leads and known suspects,” Khera said. “Like every other community, we care about the safety of our communities, and if we learn about a criminal act, we should report it to law enforcement.”

But, Khera added, the idea that Muslim Americans have special influence in such situations is like saying an Irish American had special influence with the Irish Republican Army. “It doesn’t add up,” she said.

Wednesday’s meeting was considered off-the-record, and participants declined to characterize the words of the president and other White House officials who attended — national security adviser Susan E. Rice and her deputy, Ben Rhodes, as well as Valerie Jarrett, a close general adviser who works on issues of public engagement. A brief official readout from the White House said the group discussed “a range of domestic and foreign policy issues” including health care, anti-Muslim discrimination and “the need to continue countering ISIL [the Islamic State] and other groups that commit horrific acts of violence, purportedly in the name of Islam.”

Muslim Americans had asked for the meeting for years, and the timing ultimately seemed both good and bad. Some were not happy that it was so close to the summit on extremism, because the two events would inevitably be linked in articles such as this one. But others said it was important that the meeting took place during a month in which a state lawmaker in Texas demanded Muslim visitors to her office swear an oath to the United States, and Louisiana Gov. Bobby Jindal (R) made controversial comments about Muslims in Europe.

Among broad religious groups, Muslims show the strongest support for the president, with an approval rating of 70 percent. Among racial, ethnic and religious groups, only black Protestants rate the president higher.

However, there have been disappointments for Muslim Americans. Participants at the Wednesday meeting said they raised concerns about Justice Department guidelines on racial profiling that recently were amended to ban profiling based on religion — among other things — but kept an exemption for national security.

“This administration has had a rough ride. People expected a constitutional lawyer-president to walk on water” on civil rights issues, said Berry. “No matter what would have been not enough.”

Berry praised the president’s comments at the prayer breakfast, saying they are “rooted in the right kind of tone Americans need to understand.”

She is among the Muslim American activists who interact regularly with the White House, and generally, she said, “I get the feeling they get it.” But the linking of Islam so directly and regularly to violent extremism — including, perhaps, at the upcoming summit — remains part of the mixed-bag relationship between Muslim Americans and the president.

“I think, generally, the president gets it, but does that always translate into best practices in the way the FBI trains agencies, for example. . . . These are also issues for every American. We either respect religious freedom or we don’t; it can’t be that my community is handled differently,” Berry said. “We’re the canary in the coal mine.”