Mexico’s coronavirus outbreak rose by a record 6,741 confirmed cases and 679 deaths Thursday, putting the country’s toll of 29,189 COVID-19 deaths higher than Spain’s, though the milestone was overshadowed by the resurgence in the United States.

Reacting to a spike in virus cases reported in Arizona, the top health official in the neighboring Mexican state of Sonora is asking Mexico’s federal government to temporarily close the border to non-essential visits from the U.S.

“No more crossings from the United States into Mexico for visitors who do not have essential activities,” Sonora state Health Secretary Enrique Clausen said Wednesday. “They should only be allowed for work or business.” He said he was asking only for entry into Sonora to be suspended.

Crosses and wreaths mark graves in a section of the Municipal Cemetery of Valle de Chalco opened two months ago to accommodate the surge in deaths amid the ongoing coronavirus pandemic, on the outskirts of Mexico City, Thursday, July 2, 2020. (AP PhotoRebecca Blackwell)

Crosses and wreaths mark graves in a section of the Municipal Cemetery of Valle de Chalco opened two months ago to accommodate the surge in deaths amid the ongoing coronavirus pandemic, on the outskirts of Mexico City, Thursday, July 2, 2020. (AP PhotoRebecca Blackwell)

The United States and Mexico previously agreed to limiting non-essential border crossings into the U.S. during the pandemic, but Mexico has not moved to block entry into its territory and it seemed unlikely the Foreign Relations Department would grant Clausen's request. The agency did announce it would screen incoming visitors from the United States over the July 4th weekend, checking temperatures and asking about symptoms as a preventative measure.

Several towns in Sonora are popular with U.S. visitors because they offer lower-cost health, vision and dental services. Puerto Peñasco, a resort also known as Rocky Point, is also popular with visitors from Arizona.

The Mexican state has only about one-tenth as many confirmed cases as Arizona — 8,976 as compared to 87,425 — but the two states are more comparable in COVID-19 deaths — Sonora with 909 and Arizona with 1,757.

Family members gather to mourn at the back of the hearse, as they prepare to bury a woman who died of suspected COVID-19, in a section of the Municipal Cemetery of Valle de Chalco opened to accommodate the surge in deaths amid the ongoing coronavirus pandemic, on the outskirts of Mexico City, Thursday, July 2, 2020. (AP PhotoRebecca Blackwell)

Family members gather to mourn at the back of the hearse, as they prepare to bury a woman who died of suspected COVID-19, in a section of the Municipal Cemetery of Valle de Chalco opened to accommodate the surge in deaths amid the ongoing coronavirus pandemic, on the outskirts of Mexico City, Thursday, July 2, 2020. (AP PhotoRebecca Blackwell)

Mexico's rising case numbers probably hide a much larger number of infections and deaths, because Mexico in general does very little testing.

Assistant Health Secretary Hugo López-Gatell was asked Thursday about a Washington Post story in which he was quoted as saying about three times as many people died in Mexico City from March through May than in previous years.

“I recognize that the number of people who have died from COVID-19 could be much higher here — concretely, the comment was three times as many as what we present here (at daily briefings) every night. I have said that same thing on a number of occasions,” Lopez-Gatell said.

Worker Martin Niano uses a pick to dig a grave in a new section of the Municipal Cemetery of Valle de Chalco opened two months ago to accommodate the surge in deaths amid the ongoing coronavirus pandemic, on the outskirts of Mexico City, Thursday, July 2, 2020. (AP PhotoRebecca Blackwell)

Worker Martin Niano uses a pick to dig a grave in a new section of the Municipal Cemetery of Valle de Chalco opened two months ago to accommodate the surge in deaths amid the ongoing coronavirus pandemic, on the outskirts of Mexico City, Thursday, July 2, 2020. (AP PhotoRebecca Blackwell)

On Thursday, Gov. Francisco Cabeza de Vaca of Tamaulipas, another border state, announced he had tested positive for the coronavirus, the latest in a string of Mexican state governors and federal officials who have been infected.