Washington (AFP) - President Barack Obama has urged Americans not to stigmatize Muslims following this week's deadly attacks in Brussels, saying that doing so is "counterproductive" in the fight against radical Islam.

In his weekly media address, Obama said Muslim-Americans are "our most important partners in the nation's fight against those who would wage violent jihad.

"That's why we have to reject any attempt to stigmatize Muslim-Americans, and their enormous contributions to our country and our way of life," Obama said.

"Such attempts are contrary to our character, to our values, and to our history as a nation built around the idea of religious freedom. It's also counterproductive," he said.

"It plays right into the hands of terrorists who want to turn us against one another -- who need a reason to recruit more people to their hateful cause."

Obama made his remarks as the global community continues to reel from Tuesday's attacks in Belgium, claimed by the Islamic State group, which killed 31 dead, including two Americans, and wounded 300.

"At least 14 Americans were injured, and we pray for their full recovery, along with everyone else affected by these attacks," Obama said.

The remarks by the Democratic president follow controversial statements in the wake of the Brussels bombings by the two top Republicans vying to succeed him in the White House.

Texas Senator Ted Cruz demanded this week that police "patrol and secure" Muslim neighborhoods in the US in the aftermath of the Brussels attacks, and reiterated an earlier call to suspend the relocation of Syrian refugees to the country.

Donald Trump, meanwhile, repeated his demand for the government to temporarily bar all Muslims from entering the US.

The billionaire real estate baron first called for a ban on entry into the US by Muslims back in December, following a deadly shooting attack in San Bernardino, California.