The governor's office said nearly 11,000 applications had been completed by early Friday, and 4,739 individuals or families had picked health plans and signed up for coverage.
More than 137,000 people had browsed the website and 93 percent of them went through pre-screenings to determine if they qualify for subsidized coverage or Medicaid.
Also, 166 small businesses had started applications for health insurance for employees, it said.
"That tells me that there is not only a pent-up demand, but there is an eagerness to get affordable health insurance," Beshear said.
Kentuckians who sign up before Dec. 15 will start receiving coverage on Jan. 1.
Beshear's office has kept a running tally of responses to the start of business for the Kentucky Health Benefit Exchange _ the online guide to a variety of insurance policies. Enrollment across the country began Tuesday for the exchanges, the centerpiece of President Barack Obama's health care law.Obama has mentioned Kentucky's roll-out efforts in trumpeting the new online health insurance marketplaces.
Kentucky's online system encountered some first-day glitches that temporarily delayed signing up people for coverage. Those problems were fixed later the same day, and Beshear said he was unaware of any other snafus since then.
"We are right now the gold standard in the country for implementing the Affordable Care Act," the Democratic governor said.
The health care law's critics were unimpressed.
"They can fix the website, but not the structural problems with the plans that make this an unworkable
mess," said tea party activist David Adams. He said the costs are "catching people off guard," and said "the more you analyze it, the worse it gets.""And Gov. Beshear is doing a victory tour," Adams said. "It's the epitome of brain-dead politics."
Beshear created the exchange by executive order last year. Kentucky has since received more than $250 million from the federal government to set it up.
Premiums range from less than $50 a month for a healthy single person to more than $700 a month for afamily for four. Beshear has said four out of five Kentuckians will be eligible based on income cutoffs for federal subsidies, which range from less than $100 to more than $500 a month to help pay premiums.State officials say about 640,000 Kentuckians lack health insurance in a state that ranks at or near the top nationally for many health problems.
The governor said the online marketplace offers the chance for a "transformational change" that he said will improve the state's health and productivity.
"For the first time in history, we're going to have the ability to let every Kentuckian have access to affordable health care," he said.
Beshear also decided this year to expand Kentucky's Medicaid program to cover an additional 300,000 people, most of them the working poor who have lacked health insurance coverage. The federal government will pick up the entire cost of the expansion for the first three years, and 90 percent over the longer haul.
Kentucky's Republican U.S. senators, Mitch McConnell and Rand Paul, said in an op-ed this week that the health care law that critics labeled Obamacare will result in "lost health plans, layoffs and smaller paychecks."
"As so often happens when our friends on the left set out to fix a problem, their ideas, however well-intentioned, end up hurting the very people they sought to help," the senators wrote. "That's just what we're seeing with Obamacare."
Beshear predicted that by this time next year, Kentuckians will wonder what all the fuss was from the law's critics.
"I think the critics are going to end up with a little egg on their face," he said.