Kentucky Office of Mine Safety and Licensing spokesman Dick Brown said the two miners were killed in an accident at the Dotiki Mine near Providence in western Kentucky late Wednesday.
Gov. Steve Beshear identified the miners as 27-year-old Justin Travis and 28-year-old Michael Carter.
"Our entire state mourns along with the families and friends," Beshear said in a statement. "Despite our sadness, we must press forward to the work ahead of us - fully investigating what caused this accident and determining ways to avoid such accidents in the future."
Earlier in the day, Beshear said emergency crews had reached the site of the collapse, about four miles from the mine entrance, and were "within an arm's length" of the body of a miner trapped under rock when the roof became unstable and they had to retreat.
"About that time, the roof started moving again," he said. "Rocks started falling again. And they had to pull back."
Beshear also met with family members in the Nebo Baptist Church. While he was inside, a woman was brought out of the church on a stretcher and taken away by ambulance.
Family members had declined to talk to reporters.
State and federal records show more than 40 closure orders for the mine over safety violations since January 2009.
Records show inspectors from the Kentucky Office of Mine Safety and Licensing have issued 31 orders to close sections of the mine or to shut down equipment because of safety violations since January 2009. Those records also show an additional 44 citations for safety violations that didn't result in closure orders.
MSHA records show the mine was cited 840 times by federal inspectors for safety violations since January 2009, and 11 times closure orders were issued.
The records show 214 of the citations were issued in the first four months of this year, and twice inspectors issued closure orders this year.
The accident happened while the miners were operating what's known as a continuous miner, a toothy machine that digs coal for transport to the surface, said Ricki Gardenhire, a spokeswoman for the Office of Mine Safety and Licensing.
