WASHINGTON — The Pentagon will send an additional 1,100 active-duty troops and 1,000 members of the Texas National Guard to assist in securing the United States border with Mexico, the Defense Department announced on Wednesday, in a move that would significantly expand the American military presence there.

The deployment would increase the number of American forces at the southwestern border by more than 45 percent, with the additional 2,100 troops joining roughly 4,500 personnel currently stationed there. The plan was approved on Tuesday night by Richard V. Spencer, who assumed the role of acting defense secretary on Monday while Mark T. Esper, President Trump’s latest nominee for the position, faced confirmation hearings this week.

In deploying additional troops to the border, the Trump administration continued to signal concerns about the volume of immigration, which the president has repeatedly described as a crisis. The deployment follows similar actions by Mexico, which has sent thousands of troops to its borders with both the United States and Guatemala to curb immigration in recent months, drawing praise from Mr. Trump.

“I want to thank Mexico because they really have gone above and beyond,” Mr. Trump said on Tuesday. “The borders were run by the cartels, and Mexico is taking back its country. And I give the president a tremendous amount of credit for that because that’s been going on for a long time,” he said, referring to President Andrés Manuel López Obrador of Mexico.