Democratic presidential candidate, Sen.  Bernie Sanders, I-Vt., arrives at the San Diego Convention center for a rally Tuesday, March 22, 2016.
Democratic presidential candidate, Sen. Bernie Sanders, I-Vt., arrives at the San Diego Convention center for a rally Tuesday, March 22, 2016.

The front-runners for the Democratic and Republican presidential nomination split contests with their chief rivals Tuesday in a set of western states.

Republican Donald Trump easily won Arizona and all of its 58 delegates, defeating Texas Senator Ted Cruz by more than 20 percent.

Cruz bounced back with his own resounding win in Utah.  He got more than half the vote, qualifying him for all of Utah's 40 delegates and denying Trump any portion of that total.  Cruz and the other remaining Republican candidate, Ohio Governor John Kasich, are trying to keep Trump from gaining the 1,237 delegates needed to clinch the party's nomination before its convention in July.

Democratic presidential candidate Hillary Clinton,
Democratic presidential candidate Hillary Clinton, center, speaks as Seattle Mayor Ed Murray, left, and his husband, Michael Shiosaki, right, look on Tuesday, March 22, 2016.

Vermont Senator Bernie Sanders scored two much-needed routs in the Democratic race, winning caucuses in both Idaho and Utah with more than 70 percent of the vote over former Secretary of State Hillary Clinton.

Democrats award their delegates proportionately, so Sanders has to earn lopsided victories in order to close Clinton's overall lead.  She won the Democratic contest Tuesday in Arizona by a wide margin.

Cruz on Wednesday also picked up the endorsement of former Florida Governor Jeb Bush, who dropped out of the race last month.  In a statement released by the Cruz campaign, Bush calls Cruz the only hope for Republicans to win back the White House and also criticizes Trump.

"For the sake of our party and country, we must move to overcome the divisiveness and vulgarity Donald Trump has brought into the political arena," Bush said.

Candidates react to Brussels attacks

Tuesday's voting took place in the hours after the deadly terrorist attacks at the airport in the Belgian capital of Brussels and at a subway station not far from the European Union headquarters.

Trump, who called for a temporary ban on Muslims entering the U.S. after previous attacks linked to Islamic terrorists, said he had warned about new assaults. "Brussels was a beautiful city, a beautiful place with zero crime, and now it's a disaster city," Trump said.

Republican presidential candidate Donald Trump spe
FILE - Republican presidential candidate Donald Trump speaks during a campaign rally Saturday, March 19, 2016, in Tucson, Arizona.

Kasich said the global community must "redouble" its efforts to "identify, root out and destroy the perpetrators of such acts of evil." Cruz declared that "radical Islam is at war with us," and said that if he is elected president, he would unleash the "full force and fury" of the U.S. military to defeat Islamic State jihadists.

Clinton said the U.S. must "stand in solidarity" with European allies in fighting terrorism. "We've got to be absolutely strong and smart and steady in how we respond," she said. Sanders declared, "This type of barbarism cannot be allowed to continue," saying the attack was a "brutal reminder that the international community must come together to destroy" Islamic State.

After Tuesday, Republicans have just two contests over the next three weeks, in the midwestern state of Wisconsin on April 5 and in the western state of Colorado on April 9.