A congressional House staffer holds President Obama’s fiscal 2017 budget in the House Budget Committee Room Feb. 9 on Capitol Hill. (Gabriella Demczuk/Getty Images)

President Obama sent the final budget proposal of his presidency to Congress on Tuesday, a $4.15 trillion package that will mark the closing rounds of a long-running fiscal battle with Republicans in Congress over the nation’s spending priorities.

The proposal would boost total spending by 4.9 percent, mainly as a result of increases in mandatory programs, most notably Social Security, and a rise in interest payments on the national debt. In keeping with the two-year budget deal struck with Congress in December, the president requested only a slight increase, less than 1 percent, in discretionary spending programs overall, though Republicans still accused him profligate spending.

The budget blueprint, whose cover is illustrated by the Alaskan peak Obama rechristened Mount Denali last summer, lays out programs that would not fully take effect until after he leaves office and is not expected to gain much traction on Capitol Hill. But it also includes some proposals that the administration believes can garner bipartisan support.

Under the proposal, the federal deficit would shrink to $503 billion in fiscal 2017, down from the current fiscal year but substantially more than the $438 billion figure for last year that Obama has been using when boasting about deficit reduction. In the plan, the federal deficit over the next decade would average 2.6 percent of gross domestic product, the same as its share of the economy for fiscal 2017.

A breakdown of the proposal grouped by the functions that the government performs.

Many budget experts say Obama’s proposal is as much philosophical as it is pragmatic, given the election-year politics that will shape its fate. And Republicans in Congress, who have indicated that they will not invite the Office of Management and Budget director to testify about the plan, pronounced Obama’s proposal dead on arrival.

House Speaker Paul D. Ryan (R-Wis.) said in a statement that “this isn’t even a budget so much as it is a progressive manual for growing the federal government at the expense of hardworking Americans.” He added, “We need to tackle our fiscal problems before they tackle us.”

But OMB Director Shaun Donovan said that “conventional wisdom is wrong” and that the Republicans’ refrain about the president’s budget being a non-starter was “a talking point we’ve heard every single year.” He said that “we think there are a lot of proposals that can get bipartisan support.”

One of those proposals is a major request for a 35 percent increase in cybersecurity funding to boost the federal government’s capability to defend itself against cyberattacks. The money would be spread over a variety of agencies, including the Defense Department, the FBI, the Department of Veteran Affairs and the Office of Personnel Management.

The $19 billion request, one of the largest ever sought in this area, comes after an alarming series of attacks in recent years against targets including Target, Sony, the Pentagon and the OPM.

Another proposal that may have some bipartisan appeal is to strengthen the earned-income tax credit for workers not raising children. Ryan has proposed a nearly identical measure.

Donovan said the overall budget plan would stabilize the national debt at about 75 percent of GDP. He said the budget would achieve huge savings — including more revenue than spending — amounting to $2.9 trillion in deficit reduction over 10 years compared with the current baseline. Even so, the administration projects that the deficit would grow steadily and that interest payments on the national debt would double over the next four years.

The administration’s deficit-reducing proposals include $955 billion from curbing “inefficient tax breaks for the wealthy” and closing loopholes for high- income households. It also includes $375 billion in savings on federal health-care spending, in the process extending the financial viability of Medicare by 15 years. And it assumes $170 billion over 10 years from an overhaul of immigration law, primarily from a wave of new taxpayers that would result from a bill resembling one the Senate passed in 2013.

The tax loopholes targeted for closure include one that allows wealthy individuals, in households making more than $250,000 a year, to avoid a 3.8 percent tax imposed under the Affordable Care Act by passing some investment income through partnerships or businesses.

Jason Furman, chairman of the Council of Economic Advisers, said some wealthy individuals would pay more taxes, but he said that would be because of closing loopholes rather than raising rates.

However, Obama’s budget includes a raft of controversial tax proposals that have drawn Republican fire in the past. They include taxing capital gains and carried interest at the same rates as regular income; imposing the “Buffett tax,” which would set a minimum tax rate of 30 percent on people who earn more than $1 million; restoring estate tax rates and thresholds to 2009 levels; and imposing a fee on financial institutions.

Obama also laid out a business tax plan that looks a lot like one proposed last year. It includes a 19 percent minimum tax rate on income and a 14 percent one-time tax on previously untaxed profits parked overseas.

The budget also would take aim at corporate inversions, in which U.S. firms merge with foreign ones and move their tax headquarters to the country with lower rates. The maneuver has become fodder on the presidential campaign trail. The budget would alter the ownership threshold for a company to be considered foreign for tax purposes.

Some GOP lawmakers were condemning the budget plan even before its official release.

“This budget joins his others by placing America on a fiscal path that is unsustainable and threatens our long-term economic growth.” Senate Budget Committee Chairman Mike Enzi (R-Wyo.), in a statement issued early Tuesday.

Sen. David Perdue (R-Ga.) added, “The only positive thing about this budget request is that it’s the last one we will receive from President Obama.”

The president’s budget includes a grab bag of old and new ideas, many of which have been announced in the past two weeks. Obama is asking Congress to embrace corporate tax reform and a $10-a-barrel oil “fee” phased in over five years for use on $300 billion worth of “clean tech” infrastructure.

In addition, he wants $1.2 billion to expand programs for the treatment and prevention of drug abuse, nearly $1 billion to detect and treat cancer, and $2 billion for new Pell grants for year-round students. He is seeking more money for fighting the Zika virus; combating opioid abuse; helping Puerto Rico; and toughening financial regulation by increasing the budget of the Securities and Exchange Commission and Commodity Futures Trading Commission.

Obama also proposed wage insurance, which would compensate workers who lose their jobs and end up taking ones at lower pay.

The Pentagon’s proposed budget is $582.7 billion, less than half a percentage point more than the $580.3 billion budget for fiscal 2016. It balances modernization in a force that has been at war since 2001 with the cost of operations against the Islamic State militant group, the continuing campaign in Afghanistan, and a presence in areas threatened by Russia and China.

For example, the Defense Department now needs precision-guided bombs to strike the Islamic State, while it also pursues costly long-term programs, such as the $55 billion Long Range Strike Bomber, which the Air Force wants to use eventually to replace the B-52 and other aging bombers.

The State Department’s $50 billion proposed budget includes sizable increases devoted to the fight against violent extremism in the Middle East and the world’s worst humanitarian crisis since World War II.

Obama is asking for $4.1 billion, up from $3.5 billion this year, to fund the campaign against the Islamic State and the response to the ongoing civil war in Syria. It includes programs to rebuild and stabilize towns destroyed when militants are ousted, and efforts to counter the extremists’ propaganda. With 60 million refugees or internally displaced people around the world, the budget allots $6.2 billion for humanitarian assistance, up from $5.6 billion in the current fiscal year.

Ellen Nakashima, Dan Lamothe and Carol Morello contributed to this report.