Texas governor Greg Abbott will let the state's stay-at-home order expire as scheduled on Thursday as he looks to restart the state's economy during the coronavirus pandemic.

The order will allow retails stores, malls, restaurants, movie theatres, museums and libraries to open in limited capacity on Friday.

On Monday, the Republican said: "This strategic approach to opening the state of Texas prioritises the health and safety of our communities and follows the guidelines laid out by our team of medical experts."

Businesses will be able to reopen at 25 per cent capacity.

A second phase of reopening could begin as early as 18 May if the state sees at least "two weeks of data" to confirm that there are not "flare-ups" of Covid-19.

If that stands, businesses can reopen at 50 per cent capacity.

The state is among the first to allow widespread reopening as the number of deaths in the US climbs above 55,000 and the total number of confirmed cases reaches nearly 1 million.

Julian Castro, a former mayor of San Antonio who served in Barack Obama's administration and ran an unsuccessful bid for the 2020 Democratic nomination, said that the governor's "leadership during this crisis has been weak and erratic, motivated more by politics than public health."

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He said: "Texans should follow [Centres for Disease Control and Prevention] guidance and continue to do our part to keep people safe by staying home for now and practising social distancing."

Texas Lt Gov Dan Patrick, who had suggested that senior citizens should make the sacrifice to allow the state to reopen, then doubled down on his comments and said there were more important things than living, said that "now it's time to set a new course, a course that responsibly opens up business in Texas."

"Just as we united as one state to slow Covid-19, we must also come together to begin rebuilding the lives and the livelihoods of our fellow Texans," he said on Monday.

The new order "supersedes" all local orders, as several cities and counties in the Lone State State have issued their own shelter-in-place orders.

Houston mayor Sylvester Turner said that the new order "will take these measures ... out of our hands locally" and cautioned that there is still no vaccine or sufficient testing. "The virus is still here," he said.

Austin Mayor Steve Adler had extended the capital city's stay-at-home order through 8 May.

The state's death toll has climbed to 663, according to the state's health department.