"We need to immediately halt the flow of refugees from countries with a significant al Qaida or ISIS presence. We need to empower law enforcement to patrol and secure Muslim neighbourhoods before they become radicalised," Cruz said in a statement as he joined a similar call made by Trump earlier.
Cruz, 45, said today's attacks in Brussels underscores that this is a war.
"This is not an isolated incident. This is not a lone wolf. This is a war with radical Islamic terrorism. ISIS has declared jihad on Europe and on the United States of America," he said.
In an interview to CNN, Trump reiterated his earlier call for a ban on Muslims entering the country.
"You're going to make certain exceptions, and exceptions on heads of state and some of these people and I'm not saying we don't do that," Trump, 69, said.
"But we have a real problem and people don't have any idea what's going on. We have a government that's impotent, a government that doesn't get it, it doesn't understand what's happening," he said.
Trump called for change in law to include water boarding.
"What I would do is - look, to change our law on the water-boarding thing, where they can chop off heads or drown people in heavy steel cages and we can't waterboard," he said.
"So we have to change our laws so we can fight at least on an almost equal basis. They have no laws whatsoever that they have to obey," he added.
In a statement, the Democratic National Committee (DNC) said the remarks made by Trump show that he lacks the temperament of a president.
"Donald Trump's latest comments are absurd and offensive and clearly show he lacks the temperament and reasoned decision-making we expect from our commander-in-chief," said DNC national press secretary Mark Paustenbach.
"This isn't the first time a Republican has made vast generalisations about the Muslim community. It's this type of false and divisive rhetoric that is undermining America's credibility and is putting our country's national security at risk," Paustenbach said.
Cruz is a disgrace alleged, DNC chair Debbie Wasserman Schultz.
"His comments today were worse than opportunistic and inappropriate politicking in the wake of the terrible tragedy in Brussels - they were a shameful display of hate that only serves to foment anger and make the world less secure. Barely before the smoke had cleared, he declared that - here in the US - we should institute police patrols in Muslim neighbourhoods," he said.
Democratic presidential candidate Hillary Clinton said they will be more effective in defeating radical Jihadism and defeating ISIS and the other ISIS terrorism groups if they have coalitions with nations that are predominantly Muslim.
"I don't think that you get that cooperation that I'm looking for deep, intense, long-lasting cooperation by playing these semantic games," Clinton said.
"Let's work at preventing the terrorists and isolate them from the vast majority of Muslims and defeat them and do whatever we can to protect America, Europe, and our other friends and partners around the world," she said.
Nearly 35 people were killed and over 200 injured yesterday twin bomb attacks that ripped through Brussels airport and a metro train, the latest attacks claimed by the dreaded Islamic State militant group to rock Europe.
Business Standard has always strived hard to provide up-to-date information and commentary on developments that are of interest to you and have wider political and economic implications for the country and the world. Your encouragement and constant feedback on how to improve our offering have only made our resolve and commitment to these ideals stronger. Even during these difficult times arising out of Covid-19, we continue to remain committed to keeping you informed and updated with credible news, authoritative views and incisive commentary on topical issues of relevance.
We, however, have a request.
As we battle the economic impact of the pandemic, we need your support even more, so that we can continue to offer you more quality content. Our subscription model has seen an encouraging response from many of you, who have subscribed to our online content. More subscription to our online content can only help us achieve the goals of offering you even better and more relevant content. We believe in free, fair and credible journalism. Your support through more subscriptions can help us practise the journalism to which we are committed.
Support quality journalism and subscribe to Business Standard.