The talks are proceeding months after a 35-day shutdown over the winter instigated by Mr. Trump, who had refused to sign any spending measure that did not fund a border wall.

The latest round of negotiations has been complicated by an apparent disconnect among Republicans both inside the White House and on Capitol Hill about what kind of deal to pursue. While Mr. Mnuchin declined to describe the direction of the talks, Mick Mulvaney, the acting White House chief of staff who is an ardent fiscal hawk, accused Democrats of increasing their domestic spending demands rather than moving in the administration’s direction.

“Last time I checked,” he said, “that’s not how you compromise.”

Senior Democratic officials said they had offered no new proposals on spending levels during the session, but had noted that the House had written and begun passing its appropriations bills, which added up to $647 billion in domestic spending.

The first package of those bills, approved on Wednesday, outlines funding for the Defense, Education and State Departments, and other federal agencies, totaling about 75 percent of the government. It serves as a statement of policy priorities by a Democratic majority that has struggled to move any of its marquee initiatives beyond the doorstep of the Republican-controlled Senate. A number of the provisions directly contradict policies pursued by the Trump administration.

Nestled in the nearly $983 billion spending package are provisions that would prevent the Pentagon from using funds to enforce a ban against transgender service members, prevent the State Department from spending money at Trump properties, stop funding from being used on armed sales without congressional approval, and prohibit restrictions on fetal tissue research.

It also repeals the authorization of military force passed after the Sept. 11, 2001, attacks, which granted Congress’s blessing to use military force only against nations, groups or individuals responsible for the attacks, and has been invoked for a wide array of military operations since, including in Iraq and Afghanistan. Passage of the provision is the culmination of a yearslong debate over whether to curtail the president’s war powers that has heated up in recent months.

But before lawmakers can begin to negotiate on that issue or any of the 12 spending bills to fund the government into 2020, the White House and congressional leaders must reach the broader spending agreement to prevent strict spending cuts, known as the sequester, from taking effect across every government program.