WASHINGTON — President Trump threatened on Wednesday to adopt a “warlike posture” against Democrats if they use their newly won control of the House to investigate his financial and political dealings, drawing a line at the start of a new era of divided government.

The president began a postelection news conference with an offer to work across party lines, but his conciliatory tone quickly turned contentious. And barely an hour later, he announced the firing of Attorney General Jeff Sessions in defiance of Democrats who saw an effort to impede the Russia investigation.

House Democrats also made the traditional nod to bipartisanship after their victory in Tuesday’s midterm elections even as they emphasized that they would scrutinize everything from Mr. Trump’s taxes to his campaign’s ties to Russia in 2016. But after Mr. Sessions was fired, the incoming chairman of the House Judiciary Committee said the decision would be investigated once Democrats took over in January.

[Read the latest on Jeff Sessions’s resignation.]

The instant exchange of fire indicated that there may be no lull in the conflict that has cleaved Washington during the Trump era, and if anything, it may escalate beyond what the last two years have brought. Once in control of all the levers of power in the capital, the president and his party now face the prospect of an opposition House armed with subpoena power and stocked by Democrats who won office on the promise of imposing a check on him.