As some states start to reopen businesses and lift lockdowns, the need for coronavirus testing has become a focal point, and retailers are touting renewed efforts to speed that along.

Leaders of CVS Health, Walgreens, Walmart, Rite Aid, Kroger and other companies joined President Donald Trump late Monday at the White House to announce the next phase of testing. They spoke at the podium in the Rose Garden about their plans to add new sites and increase access, especially in underserved communities and among employers trying to get back to work.

The companies laid out their plans, but some cautioned their timing and ability to ramp up will depend on having adequate supplies and lab capacity.

Some state governors have expressed frustration about not having enough swabs, reagents or lab capacity for tests, saying that's made it harder to track the coronavirus' spread and make decisions about lifting stay-at-home orders. In the U.S., there have been more than 972,900 confirmed cases of Covid-19 and at least 55,118 people have died, according to data compiled by Johns Hopkins University.

With their roots in health care, CVS and Walgreens have been two of the most active in getting sites up and running. CVS said Monday that it plans to have nearly 1,000 locations across the country by the end of May and process up to 1.5 million tests per month. Walgreens said it expects to open five more drive-thru testing locations in four more states this week and eventually open sites in 49 U.S. states and Puerto Rico.

Walmart said it will have 45 sites by the end of next week and 100 sites by the end of May. Kroger said it will expand its drive-thrus to have 50 locations in more than 12 states by the end of May.

In mid-March, Trump had a similar event with a group of retailers and health-care companies. In the Rose Garden on March 13, Walmart, Target, Walgreens and CVS committed to hosting numerous drive-thru test sites in parking lots across the country — but there were few specifics about how those sites would open or who would staff them.

As retailers worked to get the sites up and running, the companies struggled to get protective gear or communicate with government officials who were supposed to run them. In a call with reporters in mid-March, Dan Bartlett, Walmart's executive vice president of corporate affairs, said the opening of more test sites had been delayed by supply issues. He said Walmart struggled to get test kits and find masks, gloves and other personal protective gear for workers.

In late March, CVS Chief Executive Larry Merlo told CNBC that a lack of protective gear has slowed the effort.

As of Monday, Walmart has 20 testing sites, according to a map on its website. Walgreens has 18 locations across 11 states. CVS has five sites across five states. Some other companies not part of the initial pledge, including Kroger and Rite Aid, opened drive-thrus, too. Kroger currently has 30 sites. Rite Aid has 25.

Target has one drive-through testing site outside its store in Chula Vista, California, which is operated with the University of California, San Diego. A company spokeswoman said the company is still committed to providing more space but does not have medical personnel to run the sites. Its pharmacies are owned by CVS. Target did not attend Monday's White House event.

On Monday, CVS, Walgreens and Walmart acknowledged there were still factors that could slow them down.

CVS said in a news release that its plans are "subject to availability of supplies and lab capacity," and Bartlett said Walmart's ambitions are dependent on "adequate lab capacity."

Walgreens did not announce a timetable for its expansion of Covid-19 testing, saying in a news release that "the scale and timing of the overall testing expansion is dependent on the availability of tests and overall lab capacity." It said it is working with LabCorp to increase its testing capacity and eventually expects to test more than 50,000 people each week.

On Monday, it said it began to offer antibody testing at more than 100 Walgreens stores, which have LabCorp locations. The blood test can help detect whether a person has been exposed to the virus.

CVS has a total of five testing sites in five states: Connecticut, Georgia, Massachusetts, Michigan and Rhode Island. Most of the sites can do 1,000 tests per day. They are operated by CVS staff and located in large parking lots with enough space for multiple lanes, such as on Georgia Tech's campus in Atlanta and at Twin Rivers Casino near Providence, Rhode Island. They are using Abbott Laboratories' rapid testing device, which allows patients to get test results in minutes.

Most of the retailers are operating sites as drive-thrus in their store parking lots. To get a test, people must meet the criteria of the Centers for Disease Control and Prevention and make an appointment.

Correction: This article has been updated to reflect that Target has one coronavirus testing site, in Chula Vista, California.