But they disagreed - in their first debate of Campaign 2006 - on the shape of that diplomacy.
Ashdown sees China as key to success in any talks. Hatch views Beijing more skeptically.
In the debate at Ivins' Tuacahn High School, near St. George, Ashdown said any U.S. military option is, practically speaking, off the table. Even if President Bush wanted to attack North Korea, he said, he couldn't because U.S. armed forces have been spread too thin by the Iraq war.
Ashdown singled out China as vital to a diplomatic solution because Beijing has the most to lose from a nuclear North Korea. He doubted sanctions would have much effect because isolated North Korea already is so destitute.
Hatch emphasized the importance of Pyongyang joining stalled six-nation negotiations - backed by the Bush administration - that would include China, South Korea, Japan and Russia along with the United States and North Korea.
On a topic closer to home, Hatch voiced support for the Washington County land-use act, now before Congress.
He said the bipartisan Utah bill, introduced by Republican Sen. Bob Bennett and Democratic Rep. Jim Matheson, needs to be approved - now that
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Hatch noted the sale of Bureau of Land Management land outlined in the measure would increase private holdings in the county by only 1.6 percent, while allowing for more effective growth management.
"We don't need a helter-skelter approach that won't work, Hatch said.
Ashdown, the owner of Salt Lake City-based Internet-service-provider XMission, fears the bill was crafted without adequate public input. He accused Bennett - along with other elected politicians in Washington County - of crafting the legislation behind closed doors.
When will these people [politicians] stand up and say they have a conflict of interest? Ashdown asked.
Soaring health-care costs and the future of Medicare, another hot topic in southwestern Utah, home to many retirees, also surfaced at the debate.
Ashdown argued that when companies as large as Delta Air Lines and General Motors suffer because of skyrocketing health-care costs, then it's probably time for a national plan that covers all Americans.
If the cost of heath care is considered a tax, like in most of the world," he said, "then we are the most taxed people on Earth."
Ashdown labeled the health-insurance business a failure and lamented how it stymies entrepreneurs from launching small businesses.
Hatch - if he wins a sixth Senate term - said he stands a good chance of becoming chairman of the powerful Senate Finance Committee, allowing him to better serve Americans' health needs.
He stressed the importance of medical savings accounts, biomedical research and streamlined drug approvals.
mhavnes@sltrib.com