Abbott, speaking during a news conference in Austin, called the state's capacity "abundant" and said officials are "laser-focused" on maintaining that level.
The state saw another new peak Tuesday, reporting 2,518 Texans are currently hospitalized who have tested positive for the virus. Close to 15,000 beds are still open, according to the latest figures from the Department of State Health Services.
WATCH: ABC13's Tom Abrahams' one-on-one interview with Gov. Abbott
Still, the tally of hospitalizations has been on a brisk upward trajectory. Tuesday's count was up 43% from the start of the month.
The number of cases has also continued to rise in the state, and the first half of June saw some of the biggest single-day caseloads yet. Abbott said the state would reach another peak Tuesday, with officials set to report 2,622 new cases.
In seeking to explain the trend, Abbott pointed to temporary spikes in positive tests in some isolated areas. But he also suggested young people specifically are not taking the virus seriously enough, saying there are "certain counties where a majority of the people who are testing positive ... are under the age of 30, and this typically results from people going to bar-type settings."
"It's hard to tell exactly where those people contracted COVID," Abbott said. "All we know is that because these people are testing positive at a higher rate who are age 30 and under, it informs us about certain strategies to take to make sure that we are able to reduce the number of people testing positive."
Abbott pointed to a recent warning by the Texas Alcoholic Beverage Commission, which said bars and restaurants could lose their licenses for 30 days if they do not follow state guidelines to slow the spread of the coronavirus. Bars are currently allowed to operate at 50% capacity and restaurants at 75% capacity.
WATCH: Gov. Abbott suggests Texans under 30 are ignoring warning signs
The news conference featured a presentation by John Zerwas, the University of Texas System official and former state representative who is helping with the state's coronavirus response. In an exchange with Abbott, Zerwas said the state is still at "Level 5" in hospital capacity, meaning hospitals can maintain their current capacities without having to build it out.
"The bottom line is this, and that is the increased capacity of hospital beds, it does raise concerns, but as shown today, there is no reason to be alarmed," Abbott said. "Even though there are more people hospitalized, we still remain at the lowest threat level in our hospital capacity. We have plenty of room to expand beds. There are thousands of hospital beds that are available as we speak right now. And then there is the ability to surge even more hospital beds if it were ever to be needed."
As he has done in recent days, Abbott reiterated that the state still has the option to at least partially restore a ban on elective procedures to free up even more beds.
Democrats said Abbott was still botching the state's response to the pandemic on multiple fronts.
"We have to face reality: managing this crisis goes way beyond knowing how many hospital beds are available," state Rep. Chris Turner of Grand Prairie, chairman of the House Democratic Caucus, said in a statement. "Our state's positivity rates are too high and still increasing, and positive cases and hospitalizations continue to rise. And we still have yet to reach the daily testing goals Gov. Abbott set forth nearly two months ago."
Abbott has been particularly focused on the the positivity rate, or the ratio of cases to tests. The rate, presented by the state as a seven-day rolling average, increased to 8% but has since stayed below that level, registering as 6.62% on Sunday.
Disclosure: The University of Texas System has been a financial supporter of The Texas Tribune, a nonprofit, nonpartisan news organization that is funded in part by donations from members, foundations and corporate sponsors. Financial supporters play no role in the Tribune's journalism. Find a complete list of them here.
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