AUSTIN, Texas — One of the busiest trade ports on the America-Mexico border was closed Wednesday as frustration and traffic snarls mounted over new orders by the governor of Texas, Gregory Abbott, requiring extra inspections of commercial trucks as part of the Republican’s sprawling border security operation.

Since Monday, Mexican truckers have blocked the Pharr-Reynosa International Bridge in protest after Mr. Abbott last week directed state troopers to stop and inspect trucks coming into Texas. Unusually long backups — some lasting 12 hours or longer — have stacked up elsewhere along Texas’s roughly 1,200-mile border.

Not even a week into the inspections, the Mexican government said Tuesday that Mr. Abbott’s order was causing “serious damage” to trade, and that cross-border traffic had plummeted to a third of normal levels.

The gridlock is the fallout of an initiative that Mr. Abbott says is needed to curb human trafficking and the flow of drugs. Critics question how the inspections are meeting that objective, while business owners and experts complain of financial losses and warn American grocery shoppers could notice shortages as soon as this week.

Frustration is also spreading within members of Mr. Abbott’s own party: The Republican agriculture commissioner of Texas, Sid Miller, called the inspections a “catastrophic policy” that is forcing some trucks to reroute hundreds of miles to Arizona.

“I do describe it as a crisis, because this is not the normal way of doing business,” a Hidalgo County judge, Richard Cortez, whose county includes the bridge in Pharr, said. “You’re talking about billions of dollars. When you stop that process, I mean, there are many, many, many, many people that are affected.”

The shutdowns and slowdowns have set off some of the widest backlash to date of Mr. Abbott’s multibillion-dollar border operation, which the two-term governor has made the cornerstone of his administration. Texas already has thousands of state troopers and National Guard members on the border and has converted prisons into jails for migrants arrested on state trespassing charges.

Mr. Abbott warned last week that inspections would “dramatically slow” border traffic, but he hasn’t addressed the backups or port shutdowns since then. His office didn’t reply to a message seeking comment left Tuesday, but the governor planned a press conference for Wednesday afternoon in Laredo.

The disruptions at some of the world’s busiest international trade ports could pose economic and political threats to Mr. Abbott, who is seeking a third term in November. Democrat Beto O’Rourke, the former presidential candidate who is running against Mr. Abbott for governor, said during a stop in Pharr on Tuesday that the inspections were doing nothing to halt the flow of migrants and were worsening supply chain issues.

He was joined by a local businessman, Joe Arevalo, who owns Keystone Cold, a cold-storage warehouse on the border. He said that although Texas state troopers have always inspected some trucks crossing the border “they’ve never, ever, ever held up a complete system or a complete supply chain.”

An estimated 3,000 trucks cross the Pharr bridge on a normal day, according to the National Freight Transportation Chamber. The Pharr bridge is the largest land port for produce, such as leafy green vegetables, entering America.

Mexico supplies about two-thirds of the produce sold in Texas.

“We’re living through a nightmare, and we’re already suffering through a very delicate supply chain from the pandemic and to try to regrow the business,” Mr. Arevalo said.

The additional inspections are conducted by the Texas Department of Public Safety, which said that as of Monday, it had inspected more than 3,400 commercial vehicles and placed more than 800 “out of service” for violations that included defective brakes, tires, and lighting. It made no mention of whether the truck inspections had turned up migrants or drugs.

The order’s impact quickly spread beyond Texas: Customs and Border Protection officials confirmed Tuesday that there was another blockade at the Mexican customs facility at the Santa Teresa port of entry in southern New Mexico, not far from El Paso. Those protests are misguided since New Mexico has nothing to do with Texas’s inspection policies, the president of the Border Industrial Association, Jerry Pacheco, said.

He said the protests were costing businesses millions of dollars a day.

“Everybody down here is on a just-in-time inventory system,” Mr. Pancheo said. “It’s going to affect all of us, all of us in the United States. Your car parts are going to be delivered late, your computer — if you ordered a Dell or HP tablet, those are going to be disrupted.”

A professor at the McCombs School of Business at the University of Texas at Austin, Ed Anderson, compared the disruptions to those caused by February’s trucker blockade in Canada that forced auto plants on both sides of the border to shut down or scale back production. During that protest, trucks looking for other entries to cross into America wound up causing congestion at other bridges, a scenario that Mr. Anderson said might now be repeated on the southern border.

Mr. Anderson said consumers would likely begin noticing the effects by the end of this week, if not sooner.

“Either prices are going to spike or shelves are going to be low,” he said.