WASHINGTON — America will get its first taste of divided government under President Trump this week when a Democratic House tries to wrest control of the political agenda from Mr. Trump, who appears determined to keep the focus on border security, immigration and his “big, beautiful” wall.

After the midterm elections ushered in the most diverse freshman class in history, House Democrats intend to put a spotlight on the issues that worked well for them during the campaign: diminishing the influence of the wealthy and connected, expanding voting rights, lowering prescription drug costs and passing a bipartisan infrastructure bill.

Mr. Trump, on the defensive and presiding over a federal government that remains partially closed, is trying to stomp on that message. On Tuesday, as the government shutdown was in its 11th day, Mr. Trump invited congressional leaders of both parties to a briefing on border security Wednesday afternoon. White House officials did not say whether Mr. Trump would attend.

It would be the first visit by Democratic leaders to the White House since Dec. 11, when the president told Representative Nancy Pelosi and Senator Chuck Schumer he would be “proud to shut down the government for border security.”