East Baton Rouge Parish extended its mask mandate Tuesday as the parish pushed past Orleans Parish for the second most cases in the state since the outbreak began.

Amid a major testing push, East Baton Rouge has seen its case numbers nearly double since the end of June as the parish has closed the gap on Orleans, once the early epicenter of the viral outbreak.

In passing Orleans, East Baton Rouge became only the third parish to have more than 10,000 cases since the outbreak began, reporting 170 more on Tuesday to break that barrier.

Mayor-President Sharon Weston Broome announced Tuesday that her "No Mask, No Service" order will remain in effect until the parish enters Phase 3 of reopening.

"We have seen positive results since my executive order went into effect at the beginning of July, however, we still have a long way to go to protect our economy and residents," Broome said in a news release Tuesday afternoon. "Our positivity rate of those people taking COVID-19 tests has dropped since the order went into effect, but hospitalizations and new cases have risen in general."

Her current mask order, which went into effect July 3, was set to expire Aug. 3.

It’s not clear when the parish would enter Phase 3, but Gov. John Bel Edwards suggested Tuesday that Louisiana overall may be seeing the beginning signs of a plateau in new cases.

That shift, he added, may be the fruit of the partial tightening of state social distancing restrictions in Phase 2 and the statewide mask mandate.

Edwards drew that conclusion while defending those restrictions on businesses and other public activities as the best option to reduce viral spread and also avoid more severe economic limits.

“You cannot get to a transmission rate of less than one without the mitigation measures that include mandatory masks and bar closures,” Edwards said in a news conference.

East Baton Rouge Parish, Louisiana's largest by population, has closed a more than 2,500-case gap with Orleans since July 1.

East Baton Rouge hit 10,155 cases on Tuesday. Total cases in the parish were at 5,123 on June 30, state health data show.

Orleans reported 60 new cases to reach 10,071 on Tuesday. Jefferson Parish remains the top parish for total cases in the state and reached 13,780 on Tuesday.

Orleans, which has about 50,000 fewer people than East Baton Rouge does, remains ahead of the parish for cases on a per capita basis but Baton Rouge is gradually closing that gap too.

The rise in new cases in East Baton Rouge has come amid a significant push in testing in the Baton Rouge area, however.

The White House directed the U.S. Department of Health and Human Services to set up surge sites in Baton Rouge so 60,000 tests could be given in a region that federal officials had deemed a hotspot for viral spread.

With the big federal testing surge, completed tests in East Baton Rouge have nearly doubled since the end of June on a seven-day rolling average basis.

The rate of new cases per test, however, has remained nearly at or above a federal benchmark through much of July, suggesting the increase in cases hasn't been due to testing alone.

Despite the effect increased testing has on revealing new cases, Susan Hassig, a Tulane University epidemiologist, said the 10,000-case mark remains a significant threshold. Along with other data points like the recent stress on the hospitals, the case tally points to continued high prevalence of the virus in the community.

“I have been saying somewhat publicly, and certainly privately, that we should have been in Phase 1 probably three weeks ago if we’re really serious about getting this under control,” Hassig said.

The phase would further restrict businesses and public gatherings than current limits do.

Hassig added that Baton Rouge may not hold on to its ranking above New Orleans for long on total cases.

She has attributed East Baton Rouge’s gain on Orleans, in part, due to New Orleans’ early experience with the virus and more stringent city social distancing policies that have helped tamp down the virus’s spread.

But testing has also lessened in Orleans in recent months. Edwards announced on Tuesday that New Orleans was in line for a federal surge site.

“So, that’s going to once again raise the amount of testing we’re going to be doing here,” Hassig said. “So I suspect East Baton Rouge and Orleans are probably going to bounce back and forth in term of numbers of cases and, thus, their ranking.”

In East Baton Rouge, more recent statistics may be starting to point to a downward turn in the share of new cases to tests, known as positivity.

The two-day percentage on Tuesday fell to 7.8% after a large influx of tests on Monday. The parish had averaged 9.8% in weekly average positivity over the past two weeks, just under the federal benchmark is 10%. The calculations, however, do not include the date the tests were administered, only when they were reported.

Louisiana began reopening for Phase 1 on May 15-16 then moved to Phase 2 on June 5. Edwards announced on June 22 that the state, seeing an alarming increase in cases and hospitalizations, will remain in Phase 2 for 28 more days.

Email David J. Mitchell at dmitchell@theadvocate.com

Follow David J. Mitchell on Twitter, @NewsieDave.