Rev. Nick VanDenBroeke made the comments at the Church of the Immaculate Conception in Lonsdale, Minnesota.
He said in the homily that Christians needed to welcome immigrants as the Bible instructed them to welcome the stranger, but he exempted Muslims from that call.
"Both as Americans and as Christians, we do not need to pretend that everyone who seeks to enter America should be treated the same," he said. "I believe it is essential to consider the religion and worldview of the immigrants or refugees. More specifically, we should not be allowing large numbers of Muslims asylum or immigration into our country."
He went on to add that Islam was "the greatest threat in the world" to Christianity and to the United States.
VanDenBroeke also advocated for the border wall proposed by President Donald Trump, and supporter a pathway to citizenship for illegal aliens already in the country.
His comments were reported in the City Pages, which prompted CAIR to issue a statement demanding a repudiation of the message of the homily.
"We urge leaders of the Catholic Church in Minnesota to repudiate these hate-filled and un-Christian remarks as unrepresentative of the faith they hold dear," said CAIR-Minnesota director Jaylani Hussein.
Minneapolis Archbishop Bernard Hebda agreed that VanDenBroeke's comments were not reflective of the teaching of the Catholic church.
"The teaching of the Catholic Church is clear," Hebda said. "As Pope Benedict XVI noted, 'The Catholic Church, in fidelity to the teachings of the Second Vatican Council, looks with esteem to Muslims, who worship God above all by prayer, almsgiving and fasting, revere Jesus as a prophet while not acknowledging his divinity, and honour Mary, his Virgin Mother.' ... If all of us who believe in God desire to promote reconciliation, justice and peace, we must work together to banish every form of discrimination, intolerance and religious fundamentalism."
VanDenBroeke also apologized after the complaints.
"My homily on immigration contained words that were hurtful to Muslims. I'm sorry for this," he said.
"I realize now that my comments were not fully reflective of the Catholic Church's teaching on Islam," VanDenBroeke concluded.