A major boost in education funding, new police patrols in Wheaton and Germantown and a restoration of library hours are part of a nearly $5 billion operating budget unveiled Monday by Montgomery County Executive Isiah Leggett.

Leggett, who is running for a third term in the June Democratic primary, proposed a 4 percent increase in county government spending — about $159 million — for the fiscal year that begins July 1.

His budget, which now goes to the County Council, would cut the tax rate from $1.01 to 99.6 cents per $100 of assessed value, bringing the average annual property tax bill down $17. The reduction is a legal necessity: Without the trim, rising home assessments would result in Montgomery taking in more revenue than allowed by county law.

Leggett proposes to retain a tax on residential and business energy that is projected to bring in more than $200 million during the next fiscal year. The council has reduced the tax slightly in each of the past two years.

The biggest area of increased spending — and what is likely to be the thorniest political issue — is in K-12 education.

The budget includes an $80 million increase in funding for Montgomery public schools, which is $26 million more than the minimum increase required by state law. Leggett also proposed that the school system allocate $11 million from its own unspent funds on fiscal 2015 operations.

Leggett’s plan falls considerably short of the request from Superintendent Joshua P. Starr and the Board of Education; they had sought $51.7 million above minimum funding. But Leggett’s figure is in stark contrast to his proposed budget last year, which stayed at the level prescribed by the state’s minimum funding, or “maintenance of effort,” law.

Leggett said he agreed to exceed the minimum this year because the county was in somewhat better financial shape.

He added that the school system sought much more in excess of the minimum funding level this year ($51.7 million) than it had last year ($11 million), indicating a greater need.

Leggett, whose challengers in the Democratic primary include former county executive Doug Duncan and council member Phil Andrews (Rockville-Gaithersburg), has been under pressure to increase school funding from the politically influential teachers union, the Montgomery County Education Association, which makes coveted election-season endorsements for its “Apple Ballot.”

Tom Israel, the union’s executive director, said the MCEA would press the council to fund the full amount requested by the school system. Leggett’s budget “leaves us short of everything we want to do for kids,” Israel said.

The Montgomery County Council of Parent-Teacher Associations also has signaled that it has high expectations for school funding this year — and that its members would weigh officials’ actions when they vote in upcoming elections.

“I am optimistic that our local leaders will do right by our children and schools. And I know the conclusions I am going to draw before I head to the ballot box in June if the school budget is not fully funded,” Janette Gilman, the association’s president, wrote in a letter to Leggett and the council. “And I know 50,000+ Montgomery County PTA members — and registered voters — who will do exactly the same.”

Leggett said Monday that he was not swayed by election year pressures. “I’m doing what I think is right,” he said.

But political tensions were in plain view in Leggett’s Rockville office Monday as he briefed council members on the budget. Andrews renewed his long-standing opposition to what he regards as excessive spending on Leggett’s watch.

Andrews said that he objected to the extra $26 million beyond the state minimum because — barring a waiver from the state Board of Education — the county would be committed by law to spending at least as much next year.

“I think this puts the next county executive and the next County Council into a fiscal straitjacket,” Andrews said.

He also objected to the size of pay raises for police, fire and other unionized employees that Leggett negotiated last year. Combined with cost-of-living and longevity increases, the agreements average between 6.75 and 9.75 percent for the coming fiscal year.

Andrews also was critical of Leggett’s decision to retain the energy tax, first approved by the council in 2010. Leggett’s original tax proposal included a “sunset” provision that did away with the law after two years. He subsequently reintroduced a version without a sunset clause, which was approved by the council.

“Phil,” Leggett said, “We don’t need to argue over this here.”

The budget also includes a 5 percent, or $13 million, increase in public safety spending, which would pay for 23 new police officers and two forensic scientists. The officers will serve in county schools and in the rapidly urbanizing areas of Wheaton and Germantown.

Leggett’s spending plan continues the restoration of library hours that were cut during the recession. Hours at 11 branches, including ones in Chevy Chase, Damascus, Little Falls and Long Branch, will increase.

The budget also funds the new Silver Spring library, which is to open in the fall.