The Mexican government said on Thursday that it was working to reverse an order from Gov. Greg Abbott of Texas to restrict natural gas exports, part of that state’s effort to resolve widespread power outages that have left millions of Texans without electricity in the middle of a deadly winter storm.

Mr. Abbott’s order has heightened tensions between the two countries, with top Mexican officials protesting the governor’s decision to cut off gas supplies just as Mexico works to resolve its own mass power outages as a result of the frigid weather.

“We are doing our diplomatic work so that this doesn’t happen,” President Andrés Manuel López Obrador of Mexico said at a news conference on Thursday, referring to Mr. Abbott’s order. “This wouldn’t just affect Mexico — it would also affect other states in the Union.”

Governor Abbott on Wednesday ordered Texas producers who were exporting natural gas out of state to instead sell to in-state power generators until Feb. 21.

The fallout south of the border from Mr. Abbott’s measure underscored the extent to which Mexico relies on the United States for much of its power, even as Mr. López Obrador pushes for greater Mexican energy sovereignty.

Gas-fired plants generate about two-thirds of Mexico’s power. In 2019, 96 percent of natural gas imports were from the United States, according to the U.S. Energy Information Administration.

The arctic weather in Texas froze natural-gas pipelines between the two countries, according to Mexican energy officials, which, coupled with a surge in demand for gas in the United States, disrupted energy production across northern Mexico and left almost five million customers in Mexico without power earlier this week.

The mass outages affected not just private homes but also industry, with major manufacturers like General Motors and Volkswagen forced to halt operations, leading to an estimated $2.7 billion in losses, according to Reuters.

On Thursday, Mexico’s state energy company, the Federal Electricity Commission, or C.F.E., said it had restored power to all users by generating energy from other sources, including hydroelectric and coal-fired plants.

This latest outage comes on the heels of one in December that briefly left about 10 million people without electricity.

Authorities in Mexico were quick to shift the blame for this week’s outage to the country’s northern neighbor, with Mr. López Obrador hitting back at critics of the state energy company.

“Even though the problem originates in the United States, in Texas to be precise, all the criticism is toward the Federal Electricity Commission, toward the government of Mexico,” the president said on Thursday.

Mexico’s economy minister, Tatiana Clouthier, said on Twitter that she had spoken to Roberta Jacobson, a top Biden administration aide for the Southwestern border, regarding the issues confronting both Mexico and the United States because of the “emergency situation facing Texas” and said both countries were looking for “immediate solutions.”

Energy experts said the latest power blackout will add ammunition to Mr. López Obrador’s push to overhaul the energy sector and guarantee Mexican energy independence, no matter the cost to users or investors.

“Right now it’s easy to point to Texas, to the United States, to the dependence on gas imports,” said Adrián Garza Patiño, a senior analyst at Moody’s, the rating agency. “And even more so with the reaction from the government of Texas itself.”

Mr. López Obrador, who has made rebuilding both the C.F.E. and the state oil company, Pemex, a central pillar of his political and economic agenda, sent a bill to Congress this month that could quash competition from private renewable energy plants by making state-owned plants, many of which run on fossil fuels, first in line to supply the country’s power.

The proposal has been met with an outcry by business groups and environmentalists alike, with the changes likely to significantly set back Mexico’s commitment to reducing emissions by privileging coal- and oil-powered plants over privately funded renewables.

Mr. López Obrador’s political party, Morena, has a majority in both houses of Congress, but the bill’s future remains uncertain. On Monday, Mexico’s antitrust watchdog urged legislators not to approve the proposal, saying the reforms would severely stifle competition.

Later in the week, the finance committee in the Chamber of Deputies, the lower house, said the reforms could spark electricity price hikes and risked violating Mexican obligations under the U.S.-Mexico-Canada trade agreement, local media reported.

Even if the bill fails to gain traction, Mr. López Obrador’s push to dismantle energy changes that opened up the country to private investment during the previous administration could have a lasting impact on Mexico’s economy, analysts said.

“The private sector and foreign investors are concerned by the conditions for investment, or the legal uncertainty in Mexico,” Mr. Garza said. “Investors are thinking of leaving the country, or to at least stop investing any further, which is a critical element for economic growth.”