But a visit this month to a remote region of Venezuela’s vast western plains, which a Colombian guerrilla group has turned into one of the world’s busiest transit hubs for the movement of cocaine to the United States, has shown that the government’s triumphant claims are vastly overstated.

Deep in the broad savanna, one remote airstrip the government said it had disabled in a recent army raid appeared to be back in business. The remains of two small aircraft set on fire by the army had been cleared away. Traffickers working with the Revolutionary Armed Forces of Colombia, which operates with surprising latitude on this side of the border, appeared to have reclaimed the strip to continue their secret drug flights shuttling Colombian cocaine toward users in the United States.

There were no signs that soldiers had blasted holes in the runway or taken other steps to prevent it from being used again.

For years, the United States has been working with friendly governments in Colombia, Mexico, Honduras, Guatemala and other countries in Latin America, spending billions of dollars to disrupt the flow of drugs northward. But because of antagonistic relations with President Hugo Chávez of Venezuela, the reach of American drug agents, and the aid that comes with them, does not extend here.

“Our airspace has been taken over,” said Luis Lippa, a former governor of Apure State who plans to run again as an opposition candidate in elections in December. Referring to the grip of traffickers on the border region, he said, “Our national territory has been reduced.”

A map of flight tracks made by a United States government task force using data from long-range radar makes the point vividly: a thick tangle of squiggly lines, representing drug flights, originates in Apure, on Venezuela’s border with Colombia; heads north to the Caribbean; and then takes a sharp left toward Central America. From there, the drugs are moved north by Mexico’s well-established traffickers.

President Obama signed a memorandum in September that designated Venezuela, for the seventh time, as a country that failed to meet international obligations to fight drug trafficking. He cited a federal report that concluded that the country was “one of the preferred trafficking routes out of South America” and had a “generally permissive and corrupt environment.”

Venezuela says that it is caught in the middle — Colombia produces the drugs and the United States consumes them — and that it is doing all it can to fight back. In May, the government announced that the number of illicit flights it detected had been cut in half this year, although it declined to provide data to back up the claim.

“We are hitting drug trafficking hard all the time,” said Ramón Carrizalez, the governor of Apure, the border state where the drug flights originate, speaking in May at a news conference to announce the destruction of 36 hidden airfields. “Very few countries are carrying out a policy like ours.”

But the United States says Venezuela’s efforts are deeply hobbled by corruption, particularly by ties between the government and the Revolutionary Armed Forces of Colombia, known as the FARC, which controls much of the cocaine traffic in the region.

Since 2008, the Treasury Department has accused at least seven high-level military officers and current and former officials in Mr. Chávez’s government of aiding the FARC, and sometimes exchanging weapons for drugs. Defense Minister Henry Rangel Silva was one of those singled out by Treasury officials. Venezuela dismissed the accusations as imperialist meddling.

The White House Office of National Drug Control Policy estimates that as much as 24 percent of the cocaine shipped out of South America in 2010 passed through Venezuela, accounting for more than 200 tons.

More than half of that left from the hidden airfields in Apure, analysts say. They say that Venezuela’s central role as a transit point for drug shipments began after Mr. Chávez halted cooperation with the United States Drug Enforcement Administration in 2005, accusing its agents of spying.

Around the same time, Colombia, with assistance from the United States, began to tighten control of its airspace.

As a result, the traffickers jumped across the border to Apure, where an airstrip can be fashioned on the flat prairie in a few hours by dragging a log behind a pickup truck to smooth the ground.

“You can blow up an airfield here and it doesn’t matter,” said one resident, standing beside an eight-foot-deep hole that soldiers had blown in a runway near the Cinaruco River, the plains stretching out for miles. “They can make another one right next to it.”

But perhaps the main attraction for traffickers is that the federal government’s hold on large parts of Apure, the poorest state in the country, is tentative at best.

In many areas, residents say, the real power is held by the FARC, which they describe as moving around the state with alarming impunity.

One resident living in Santos Luzardo National Park, a picturesque preserve abounding in wildlife, said that last month two FARC members patrolled the remote area on motorcycles, asking farmers if they had heard any airplanes, apparently concerned that traffickers were using a nearby airstrip without paying.

The guerrillas also collect protection money from local businesses, ranchers and fishing camps along some parts of Venezuela’s long border with Colombia. One resident said that a small group of FARC members showed up at a homestead in December and set up camp for a week, using it as a base to patrol the area and possibly protecting drug flights. He said the owner had no choice about whether to accept, although the guerrillas brought their own food.

The residents also expressed fear and mistrust of government authorities. Most said they believed that local officials and soldiers were in league with the traffickers and that passing along information about the traffickers’ activities would result in reprisals. Residents said they had learned to coexist with the traffickers just as they had gotten used to the frequent sound of low-flying aircraft at night. But many said they were fearful and felt intimidated.

“We all knew what was going on, but no one said anything,” a man said of the smugglers who used a local airstrip. “What were we going to do about it? The one that should be doing something is the government. They should be constantly patrolling the area.”

*Meridith Kohut contributed reporting from La Macanilla; María Eugenia Díaz from Caracas, Venezuela; and Jenny Carolina González from Bogotá, Colombia.