Republican front-runner Donald Trump calls Brussels "a disaster," the morning after deadly blasts rocked the Belgian capital. Democratic front-runner Hillary Clinton urges the U.S. to "reaffirm our solidarity with your European friends." (Sarah Parnass/The Washington Post)

This post has been updated.

Republican and Democratic presidential candidates delivered sharply contrasting responses to the deadly terrorist attacks that shook Brussels on Tuesday, with the GOP contenders fiercely criticizing President Obama's national security policies and voicing support for a more aggressive posture, and the leading Democratic hopeful's campaign warning against "advocating torture or bigotry."

The reactions, coming on a day when three more states will hold nominating contests, mostly mirrored the input the candidates have offered in response to previous attacks, such as the massacre in Paris last fall. They contained little in the way of policy specifics and they also raised the possibility of deepening fault lines between and within the two political parties.

Sen. Ted Cruz (R-Tex.) issued a statement arguing that the United States should "empower law enforcement to patrol and secure Muslim neighborhoods before they become radicalized." Later, Cruz's campaign said that law enforcement agencies should target terrorism as they do threats from gangs and human trafficking.

"We know what is happening with these isolated Muslim neighborhoods in Europe. If we want to prevent it from happening here, it is going to require an empowered, visible law enforcement presence that will both identify problem spots and partner with non-radical Americans who want to protect their homes," Cruz spokeswoman Alice Stewart said.

Speaking with reporters in Washington, Cruz accused Republican front-runner Donald Trump of wanting to withdraw the United States from NATO.

"NATO should join with the United States in utterly destroying ISIS," Cruz told reporters, using an acronym for the Islamic State, "and I would note that NATO is ready to act in a way that our president is not."

Republican presidential candidate Donald Trump leads reporters on a tour at the at the Old Post Office, soon to be a Trump International Hotel, in Washington. (Jabin Botsford/The Washington Post)

Trump has not said that the United States should withdraw from NATO, but he questioned U.S. involvement in the organization and said in an interview with The Washington Post editorial board that it may need to be diminished in the future.

On Twitter, Trump sought to belittle Obama, who spoke about the Brussels attacks from Cuba, where he is making a historic visit. "President Obama looks and sounds so ridiculous making his speech in Cuba, especially in the shadows of Brussels. He is being treated badly!" Trump tweeted.

Trump also tweeted that he has "proven to be far more correct about terrorism than anybody," adding that he hopes voters in Arizona and Utah, the two states holding Republican and Democratic contests Tuesday, would support him. In addition, Idaho is holding Democratic caucuses.

Ohio Gov. John Kasich (R), speaking on MSNBC, said Obama "ought to return home" to coordinate a response to the attacks with foreign leaders.

The Islamic State claimed responsibility for attacks at a Brussels airport and metro station, which have left more than 30 dead.

In a statement, Democratic front-runner Hillary Clinton said: "These terrorists seek to undermine the democratic values that are the foundation of our alliance and our way of life, but they will never succeed. Today's attacks will only strengthen our resolve to stand together as allies and defeat terrorism and radical jihadism around the world.”

Sen. Bernie Sanders of Vermont issued a similar statement, saying: “Today's attack is a brutal reminder that the international community must come together to destroy ISIS. This type of barbarism cannot be allowed to continue.”

A tweet from Clinton's account voicing some warning — but without mentioning the attacks — said: "We can be strong and smart without advocating torture or bigotry. We will not let fear dictate our foreign policy." It was not signed "-H" — an indication that she did not directly write it.

Ibrahim Hooper, a spokesman for the Council on American-Islamic Relations, shot back against Cruz's statement about patrolling "Muslim neighborhoods."

"It's really beyond belief that you have one of the leading presidential candidates calling for law enforcement to target religious communities totally based on the fact that they are of a particular faith," he said. "In normal times, this would be the sort of thing that would disqualify someone from running for dogcatcher, much less president of the United States."

David Weigel contributed to this report