Secretary of State Marco Rubio will deliver a strong message from President Trump to Colombia’s new president when he pays him a visit this week, according to two people with knowledge of the trip.

The message: Eradicate cocaine and dismantle trafficking groups.

The Trump administration is embarking on a militarized anti-cartel push it has likened to the offensive against Al Qaeda and the Islamic State as it seeks to exert greater control in Latin America.

Colombia, the world’s largest cocaine producer, has in recent years seen a surge in production amid soaring global demand for the drug. That has set off a spike in violence as armed groups battle to control territory and move into neighboring countries like Ecuador and Venezuela.

In Abelardo De La Espriella, Colombia’s recently elected president, President Trump may find an eager partner.

Mr. De La Espriella, who made crushing “narcoterrorists” a central plank of his outsider campaign, has touted military operations against trafficking groups in his first month in office. As Mr. Rubio prepared to visit, the new Colombian leader posted images of body bags holding what he said online were slain group members.

Since the day Mr. De La Espriella was inaugurated, when the United States announced a $1 billion dollar aid package for Colombia, he has enrolled Colombia in the Trump administration’s new security alliance, the Shield of the Americas, and pledged to make the country its regional hub. He has also committed to allowing joint military operations with the United States.

The secretary of state plans to press Mr. De La Espriella to eradicate hundreds of square miles of coca crops, an issue described as a priority for Mr. Trump, the people with knowledge of his trip said. The Colombian leader will also be asked to to further deploy Colombia’s security forces and to target armed groups’ financial network. The two people spoke on the condition of anonymity to discuss diplomatic matters.

Mr. Rubio and Mr. De La Espriella are also expected to discuss Colombian military capabilities. While Colombia has long had one of the most advanced militaries in the region, experts say it has been hobbled by funding cuts, a diminished helicopter fleet and a lack of equipment like drone protection systems.

Gimena Sánchez, Andes director for the Washington Office on Latin America, said that along with joint operations against traffickers, Mr. De La Espriella was likely to bring up the promised aid package during the Rubio visit. He may also broach the possibility of the Trump administration reducing tariffs on Colombia and providing more help with rebuilding efforts following last month’s devastating earthquake.

In response to detailed questions, the State Department referred to the announcement of Mr. Rubio’s trip. One aim, it said, was “enhanced cooperation in the shared fight against narcoterrorism.”

In Mr. Trump’s second term, his administration has zeroed in on the drug trade, justifying deadly strikes against people the administration claims are traffickers — often without evidence — by designating them as terrorists.

The second Trump administration has added about 20 new Latin American groups to a list of foreign terrorist organizations. They include transnational gangs like Venezuela’s Tren de Aragua; dissident factions of a once-powerful rebel group in Colombia, the Revolutionary Armed Forces of Colombia, known as FARC; and warring drug gangs in Ecuador.

Last month, Gen. Francis L. Donovan, the commander of the United States Southern Command, traveled to Colombia and Ecuador to discuss joint operations — which both countries have authorized — and the risk that targeting Colombian traffickers could push more of them across Ecuador’s border.

Ms. Sánchez, the regional expert, said that while civilians had paid a toll in recent years as clashes between armed groups worsened, it could become still more dangerous for them if more military forces are deployed. That could also lead to rights violations, she said.

And increasing pressure to eradicate coca crops poses health risks, Ms Sánchez said. In 2015, Colombia stopped aerial fumigation following a World Health warning about the health effects of the herbicide used to kill coca plants, glyphosate.

Ms. Sánchez said she was concerned about the resumption of aerial fumigation, even if it was with another chemical. “It has environmental and health consequences and gets rid of people’s food crops,” she said. And to residents, she said, “it feels like it’s an invasion.”

Mr. Rubio also plans to address trade relations with China during his visit. The United States is seeking to bring more of Latin America under its control and to create conditions favorable to American investment.

Last month, Ecuador’s president, Daniel Noboa, traveled to China to meet with leaders, a move that risked rankling U.S. officials. Ecuador’s economy is deeply enmeshed with China, which financed a major hydroelectric dam project and is the largest buyer of Ecuadorean shrimp. Mr. Noboa told reporters that business with China had to continue.

Peru, led by the recently elected President Keiko Fujimori, also has extensive trade ties with China.

Mr. Rubio is also expected to seek commitments from leaders related to migration and deportations, according to the people familiar with his agenda.

José María León Cabrera contributed reporting from Quito, Ecuador.