The massive $1.1 trillion spending bill would fund federal agencies through the rest of the fiscal year. (Karen Bleier/AFP/Getty Images)

Congressional negotiators unveiled a $1.1 trillion funding bill late Monday that would ease sharp spending cuts known as the sequester while providing fresh cash for new priorities, including President Obama’s push to expand early-childhood education.

The 1,582-page bill would fully restore cuts to Head Start, partially restore cuts to medical research and job training programs, and finance new programs to combat sexual assault in the military. It would also give all federal workers a 1 percent raise.

But in a blow to the District, it provides only partial funding to continue constructing buildings for the Department of Homeland Security’s campus in Anacostia.

The White House and leaders of both parties praised the measure, which would fund federal agencies for the remainder of the fiscal year and end the lingering threat of a government shutdown when the current funding bill expires at midnight Wednesday.

“The bipartisan appropriations bill represents a positive step forward for the nation and our economy,” White House budget director Sylvia Mathews Burwell said in a statement.

The spending bill puts flesh on the bones of a bipartisan budget deal struck in December, when Republicans and Democrats agreed to partially repeal the sequester, heading off a roughly $20 billion cut set to hit the Pentagon on Wednesday and restoring funding to domestic agencies, which had already absorbed sequester reductions.

Despite the increases, the bill would leave agency budgets tens of billions of dollars lower than Obama had requested and ­congressional Democrats had sought. That represents a victory for congressional Republicans, who, after three years of fevered battles over the budget, have succeeded in rolling back agency appropriations to a level on par with the final years of the George W. Bush administration, before spending skyrocketed in an effort to combat the recession.

Rep. Tom Cole (R-Okla.), a senior member of the House Appropriations Committee, said he expects a majority of lawmakers in both parties to support the measure.

“Everybody can find something to complain about — legitimately so,” Cole said. “But from the Republican standpoint, gosh, this is $164 billion less than Bush’s last discretionary budget, so that’s pretty good progress in cutting spending.”

Many Democrats agreed.

“Compared to the sequester, this is obviously a big improvement. But compared to investments we should be making, it falls far short,” said Rep. Chris Van Hollen (Md.), the senior Democrat on the House Budget Committee. The measure proves, he said, that “this notion that the federal government is on a spending binge is just nonsense.”

With the deadline for a government shutdown fast approaching Wednesday night, House and Senate leaders were preparing a temporary bill to keep the government open through Saturday. That would give lawmakers the rest of the week to review the massive new measure, which proposes funding and policy changes that would reach into every corner of the federal government.

House Appropriations Committee Chairman Harold Rogers (R-Ky.) and Senate Appropriations Committee Chairman Barbara A. Mikulski (D-Md.) met through the weekend to put the finishing touches on the package. The pair released a joint statement late Monday, along with a photo showing them smiling happily and shaking hands.

“As with any compromise, not everyone will like everything in this bill,” the statement said. “But in this divided government a critical bill such as this simply cannot reflect the wants of only one party.”

Given barely a month to complete work on the package, Mikulski and Rogers were able to overcome early partisan disputes over funding for the Affordable Care Act, Obama’s signature legislative achievement, and payments due to the International Monetary Fund, a frequent target of conservatives. To sweeten the package, they agreed to include a provision that would exempt disabled veterans from a modest pension reduction for military retirees enacted last month to help cover the cost of the sequester repeal.

All told, the bill would provide $1.012 trillion to the Pentagon and other federal agencies. An additional $92 billion would be set aside for overseas operations, including military activity in Afghanistan and assistance for the growing flow of refu­gees fleeing the war in Syria. The bill also authorizes $6.55 billion for domestic disaster relief.

The measure authorizes a 1 percent pay increase for civilian federal workers and U.S. military personnel. But in response to several examples of excess spending by federal agencies, the bill would put in place new limits on certain conferences, official travel and employee awards.

The National Institutes of Health would receive $29.9 billion, $1 billion more than under the sequester but $714 million less than the agency was due to receive last year before the sequester hit last March.

Carrie Wolinetz, president of United for Medical Research, a consortium of patient, provider and research organizations, said the proposal “won’t adequately reverse the damage done by last year’s budget sequester and ensure the nation’s biomedical research enterprise makes continued progress in lifesaving research and development.”

Head Start, which had to drop children from its rolls due to the sequester, would get $8.6 billion, fully reversing the cuts. And while Republicans refused to finance Obama’s push for universal pre-kindergarten classes, they granted his request to expand Head Start partnerships that benefit toddlers and infants.

The Department of Homeland Security would face a reduction in funding of about $336 million, with most of the cuts at the scandal-ridden Transportation Security Administration. In a victory for Republicans who have sought for years to boost the use of private security contractors, the agreement increases funding for private security screeners and caps the TSA’s overall screening personnel at 46,000.

The agreement is riddled with dozens of controversial policy riders. One would bar funding to enforce a law that requires incandescent light bulbs to meet new efficiency standards.

The measure would continue a ban on transferring terrorism detainees at the detention facility at Guantanamo Bay, Cuba, to sites in the United States. It would also withhold additional funding for the government of Afghanistan until the country agrees to a new bilateral security agreement. And the measure would ban foreign aid for Libya until Secretary of State John F. Kerry “confirms Libyan cooperation” with ongoing investigations into the Sept. 11, 2012, attack at the U.S. diplomatic outpost in Benghazi.

The measure would also provide new congressional backing for Obama’s strategy of continuing aid to Egypt, despite a law that forbids U.S. military aid to governments that have taken power by military coup, as Egypt’s interim military-backed government did in July.

Several issues regarding gun control are also included in the bill. The legislation restricts the Justice and Homeland Security departments from establishing programs similar to the “Fast and Furious” gun-tracking effort. In response to allegations that the administration has been stockpiling ammunition for use by federal agents, the measure also requires Homeland Security to provide detailed reports on its purchase and use of ammunition.

The measure also continues a ban on the use of federal funding to perform most abortions, including abortions in the District and for federal prisoners. But Republicans agreed to jettison other contentious proposals, including a ban on new federal regulations for greenhouse gases and the “global gag rule,” which sought to prohibit U.S. funding for organizations that give women information about abortion.

Anne Gearan contributed to this report.