Democratic presidential candidate Hillary Clinton speaks at Saban Forum 2015 in Washington, Dec. 6, 2015.
Democratic presidential candidate Hillary Clinton speaks at Saban Forum 2015 in Washington, Dec. 6, 2015.

WASHINGTON - U.S. presidential candidates sparred Sunday on the best way to combat Islamic State terrorism in the wake of last week's deadly massacre at a holiday gathering for local government workers in California.

The leading 2016 Democratic contender, former Secretary of State Hillary Clinton, told ABC's This Week interview program that a "much more robust air campaign" needs to be launched against Islamic State targets in Iraq and Syria. She said the United States needs "much better help" from Sunni and Kurdish groups on the ground fighting the insurgents, but ruled out sending in U.S. ground forces, as has President Barack Obama.

"Where I sit right now," Clinton said, "I think that would make things worse."

Social media outlets

In addition, she called for online social media outlets, such as Facebook, Twitter and YouTube, to ban militants from communicating on the sites, saying they "cannot permit the recruitment and the actual direction of attacks or the celebration of violence." One of the California attackers, Pakistani national Tashfeen Malik, used Facebook during the attack in which she and her husband killed 14 people to vow her allegiance to Islamic State leader Abu Bakr al-Baghdadi.

Clinton stopped short of calling for a ban on the sale of encryption software that some terrorist suspects are believed to use to thwart law enforcement monitoring of their activities. She said she believes "the best minds" from technology companies and the government can work together to find ways to successfully monitor plans for more terrorist attacks.

Donald Trump

The leading Republican presidential contender, billionaire real estate mogul Donald Trump, told CBS's Face the Nation that he would be open to racial profiling and investigating the families suspected of terrorism.

He said he would be "very tough on families," and would "go after the wives" of attackers.

Republican presidential candidate Donald Trump spe
Republican presidential candidate Donald Trump speaks during a campaign rally, Dec. 5, 2015, in Davenport, Iowa.

Trump, a political novice, has soared to a lead among Republican voters over other party candidates who are current and former senators and governors. He said it is wrong for people who suspect a possible attack is being planned to fail to alert law enforcement officials for fear of "racial profiling" someone. He said that is not playing on fears, but rather "playing on common sense."

Chris Christie

But another Republican candidate, New Jersey Governor Chris Christie, rebuffed Trump's profiling suggestion, telling CBS's Face the Nation, "The fact is we do not need to be profiling in order to be able to get the job done here.  What you need is a president who has had the experience and the know-how to do this and not someone who is just going to talk off the top of their head.”

Republican presidential candidate, New Jersey Gov.
FILE - Republican presidential candidate, New Jersey Gov. Chris Christie responds to a question during the Republican presidential debate, Sept. 16, 2015.

Jeb Bush

Republican contender Jeb Bush, a former Florida governor and the son and brother of two U.S. presidents, told ABC that Islamic State fighters "are at war with us. We need to destroy them." He called for directly arming Kurdish fighters and creation of a no-fly zone in Syria, a plan similar to what Clinton is calling for.

Republican presidential, former Florida Gov. Jeb B
FILE - Republican presidential, former Florida Gov. Jeb Bush speaks at the Republican Jewish Coalition Presidential Forum in Washington, Dec. 3, 2015.

But he said it was wrong to dismiss the idea the United States is fighting "radical Islamic terrorism.  This is a fight for Western civilization."

Clinton said that to use the term "radical Islam" makes it sound "like we are going after the religion.  It does not speak to the vast number of peaceful Muslims here and throughout the world."

Clinton, the country's top diplomat from 2009 to 2013 during President  Barack Obama's first term, attacked the Republican-led defeat in the Senate last week of a measure to ban the sale of handguns to people whose names are on the country's no-fly list.

But Bush said the no-fly list has proven to be imprecise, on occasion mistakenly listing names of Americans who have no connection to terrorism.  He said those directly connected to terrorism investigations should be barred from buying guns.