Amid nationwide marches, highway blockades and looting stemming from widespread outrage over an increase in gas prices, President Enrique Peña Nieto of Mexico went on national television to appeal for understanding.

With international oil prices rising and Mexico dependent on gasoline imports, he argued in the speech on Thursday, the government had no alternative but to raise prices at the pump. “Here I ask you,” he said, gesturing at the camera, “what would you have done?”

It did not take long for him to get an answer, as social media erupted with suggestions and disgust.

Combat corruption and impunity. Eliminate gasoline vouchers for elected officials. Collect more taxes from multinational corporations. Cut the salaries and benefits of high-level government officials. Sell the presidential plane. Reduce the first lady’s wardrobe spending. Resign.

It was a tough week for the president, who seems to be trapped in a slow, downward spiral of unpopularity, with two more years left in his term and Mexico reeling from myriad problems including rampant corruption, resurgent homicide rates, a thriving drug trafficking industry, a sluggish economy and a plummeting peso.

The few voices of support for Mr. Peña Nieto — in political circles and among news commentators — have been drowned out by his detractors, and no more so than in the past week, when discontent over the gas price increase boiled over into protests and looting, setting off clashes with security forces that left several dead around the country.

The unrest comes as Mexico braces for the administration of President-elect Donald J. Trump, who has threatened to introduce far more restrictive immigration and trade policies, including canceling the North American Free Trade Agreement, increasing deportations and building a wall on the southern border of the United States.

Concern in Mexico about Mr. Trump’s planned tack on trade has been so great that he has been able to move the markets on the basis of his Twitter posts.

The Mexican peso hit record lows last week after he criticized General Motors on Twitter for exporting cars made in Mexico and Ford Motors announced that it would cancel plans for a $1.6 billion plant in the country. Mexico’s Central Bank was forced to intervene to bolster the peso, but the currency took another hit after Mr. Trump threatened Toyota on Thursday with a “big border tax” if it went ahead with a new factory in Mexico.

Mexico’s Economy Ministry issued a brief statement in response saying the government “rejects any attempt to influence investment decisions by companies based on fear or threats.”

But in general the Peña Nieto administration seems to be struggling to figure out how to respond to Mr. Trump. Mexicans have been clamoring for a full-throated, chest-out defense of their country and sovereignty against Mr. Trump’s threats, but many say they have yet to hear it.

Confidence in Mr. Peña Nieto is so low — approval ratings have sunk below 25 percent — that he appears to be struggling to sell anything to the public, most recently the gas price increase last week.

“Such a low level of popularity reduces his capacity to gather support or his margin for action to reactivate the economy,” said Ignacio Marván, a political analyst at CIDE, a Mexico City university.

Mr. Peña Nieto’s efforts have been handicapped, analysts say, by a seeming disconnect from the public mood.

The government looked unprepared for the violent responses to the price increases, which took effect on New Year’s Day, when most officials were on vacation. Mr. Peña Nieto himself was in the middle of a golfing trip. And as bloody unrest swept across the country, the president kept silent, finally making a public statement on the issue on Wednesday.

Even then, his comments were buried in a news conference focused on cabinet changes that included the return of Luis Videgaray, a close confidant who resigned under pressure as finance minister in September after championing an unpopular visit by Mr. Trump to Mexico.

The administration’s detached response to the upheaval contributed to the impression of a president out of touch with the population, analysts said, and gave a sense of a leadership that is adrift, blindsided by events.

The gas price increases of about 20 percent are part of a broad overhaul that ends the state’s monopoly over the energy industry. The government has long controlled and subsidized gasoline prices, but by the end of the year it will allow gas prices to fluctuate according to the market, a move intended to attract foreign investment to compete with the state oil company, Pemex.

The government has argued that ending fuel subsidies will help the country avoid spending cuts to social programs, and that the subsidies have disproportionately benefited wealthier Mexicans who own cars. But many fear that higher gasoline prices will increase costs for food and public transportation, hitting the pocketbooks of even the poorest Mexicans.

Though Mexico’s opposition parties are now condemning the price increase, most of them voted for it as part of the budget approved in October. But Mexico imports more than half of its gasoline from the United States, and Mr. Trump’s election sent the peso to a historic low, raising the price of imported gasoline in pesos greater than anybody expected.

Analysts said the government could have forestalled the fallout by designing measures that would have softened the blow for poorer Mexicans, or by creating subsidies for truck drivers or owners of older vehicles.

“They didn’t think about it,” said Vidal Romero, a political analyst at the Autonomous Technological Institute of Mexico. “There is no compensation for citizens.”

Ignited by the gas price increase, but fueled by broader discontent with the government and uncertainty about the country’s direction, citizens took to the streets, staging marches throughout the country and blocking key highways.

Criminals also used the cover of the protests to break into stores and malls to strip shelves bare of home appliances, electronics, food and toys.

By last weekend, hundreds of stores had been looted around the country and more than 1,000 people detained, the authorities said, and at least six people had been killed in clashes between looters and the police.

The administration has rejected calls to rescind the price increase, and the ruling Institutional Revolutionary Party traded accusations with opposition groups about responsibility for fomenting the disorder.

With Mr. Peña Nieto’s credibility so diminished, it will be impossible for the president to accomplish much before the 2018 presidential election, analysts said. He is not eligible to run again.

The contrast with the early days of Mr. Peña Nieto’s presidency is remarkable. When he took office four years ago, his sharp political instincts helped push a bold reform agenda through Congress with support from the opposition. The reforms included the opening of the traditionally closed energy sector to foreign investment, an exceptional political accomplishment given the Mexican public’s view of the oil industry as a bedrock of the national patrimony.

But now those instincts appear to have been eroded by scandal and mismanagement, and perhaps by an insulation from emotions on the street.

“He has lost his feeling for politics,” Mr. Romero said.

The president’s perceived weaknesses and his low approval ratings have opened up space for opposition groups and cast the future of his party’s influence into doubt. Even the Institutional Revolutionary Party’s longstanding dominance in the president’s home state, the populous State of Mexico surrounding Mexico City, has been thrown into question, with the state’s governorship up for grabs this summer.

Perhaps the biggest political beneficiary of Mr. Peña Nieto’s declining popularity has been the populist politician Andrés Manuel López Obrador, a former mayor of Mexico City, who is leading in polls of potential candidates for the 2018 presidential contest. With each misstep of the president, Mr. López Obrador seems to become even more popular; some political observers refer to Mr. Peña Nieto as Mr. López Obrador’s “campaign manager.”

The looting and criminal unrest across the country had subsided by the weekend, but protests continued, with thousands taking to the streets in largely peaceful marches.

“We don’t want this corrupt country any more,” said Alicia Rios, 32, a receptionist who joined thousands of protesters for a march through downtown Mexico City on Saturday. “The legislators get 10,000 pesos in gasoline vouchers when the people can’t afford to fill up their tanks.”

She added, “If gasoline goes up, everything goes up.”