Ted Cruz has been lambasted after his team of national security advisors included Frank Gaffney, known for his extreme views on Islam.

Gaffney was introduced on Thursday as part a "high profile" coalition of experts to give the Republican presidential candidate counsel on foreign policy. The former advisor to Ronald Reagan's administration founded the think-tank Centre for Security Policy, which has been labelled an anti-Muslim "hate group" by a civil rights organisation.

Cruz said he would reverse what he described as the weakening of the United States in a dangerous world. He singled out militant Islamist groups in the Middle East and north Africa as his focus.

Gaffney, who once wrote an op-ed for the Washington Times that suggested President Obama was a Muslim, has been labelled a fringe conspiracy theorist.

The Southern Poverty Law Centre, a civil rights organisation that monitors US extremist groups, has labelled the Centre for Security Policy a "hate group" and Gaffney a "notorious Islamophobe."

The organisation's president said: "It's a terrible mistake for anyone to seek advice from Frank Gaffney on matters of foreign policy or must of anything else for that matter.

"His world is one of conspiracy, where the Muslim Brotherhood is infiltrating the highest reaches of our government and our country is on the verge of adopting Sharia law," he said according to the New York Times.

Gaffney did not respond to a request for comment, but a spokesman pointed to online essays where Gaffney has rejected such criticism, saying his group is a defender of civil liberties against "Islamic supremacists".

The Council on American-Islamic Relations (CAIR), a Muslim rights group, urged the conservative Christian candidate to reconsider having Gaffney and others who have made anti-Muslim remarks as his advisers, saying it suggested Cruz entertained "anti-Muslim bigotry".

Besides Gaffney and his think-tank colleagues, CAIR said Cruz should drop William Boykin, a retired US Army lieutenant general who has said the government should be allowed to ignore the US Constitution to pass laws limiting Muslims' right to freedom of speech and religion.

Some of Cruz's other advisers have been critical of anti-Islamic rhetoric, including Abrams and Mary Habeck, another former Bush adviser; both have said Islam should not be demonized.

Another adviser is Katherine Gorka, president of the Council on Global Security, a group that produces research on Islamist violence, who said in an email that Cruz "understands the vital role that America's military strength plays across the globe but without wanting to engage the US in expensive democracy-building adventures."

Additional reporting from Reuters.