House budget leaders will propose a two-year plan Sunday that gives hospitals an extra $81 million but not the Medicaid expansion many of them are seeking.

The House Appropriations Committee also plans to plow an extra $47 million into mental-health services and increase funding to the state’s free health clinics by $6 million, or 50 percent.

That money — especially the $81 million to help community and teaching hospitals cover inflation expenses — will be offered as an olive branch to those lobbying to expand Medicaid under the new federal health-care law.

“We feel that it’s a very solid budget that should be well received by both sides of the aisle,” said Del. S. Chris Jones (R-Suffolk), chairman of the Appropriations Committee.

The GOP-dominated House remains strongly opposed to adding 400,000 more Virginians to the federal-state health program for the poor and disabled, contending that Washington cannot afford to keep its promise to bankroll most of the $2 billion-a-year cost.

But House budget leaders also do not want to seem insensitive to the demands of hospitals, the largest employers in some rural regions of the state. They highlighted their plans for higher hospital, clinic and mental-health funding in a briefing with reporters Friday, ahead of formal votes the committee will take on the plan Sunday afternoon.

The Senate Finance Committee also will meet Sunday to vote on its own budget plan. Senate leaders did not offer a preview of their spending proposal, but it is no secret that it will call for expanding Medicaid.

Democrats and several moderate Senate Republicans favor expansion, as does Gov. Terry McAuliffe (D), who says it will provide health care to needy residents and create more than 30,000 jobs — all with federal tax dollars that Virginians are already paying.

McAuliffe has said that some hospitals will be forced to close without expansion because they lost reimbursements under the federal Affordable Care Act for some charity care that new Medicaid enrollments were intended to cover.

Committees from both chambers have based their budgets on the two-year, $96 billion spending plan that Gov. Robert F. McDonnell (R) proposed shortly before leaving office. They will vote Sunday to amend McDonnell’s plan to their liking, then send their versions to their respective chambers. Ultimately, the rival House and Senate plans will go to a conference committee tasked with hammering out the differences.

Under the ACA, eligibility for the Medicaid program would be greatly expanded. The federal government has promised to pay the full cost — $2 billion a year in Virginia — for the first three years and 90 percent after that.

McDonnell’s plan called for increasing Medicaid spending by $674 million, but only to keep pace with inflation and enrollment under current eligibility criteria. He did not call for expanding Medicaid, and he included language that would sunset any expansion in June 2016.

Some pro-expansion legislators saw that as an opening, but others viewed it as an added defense against broadening the program.

Both the House and Senate will call for ripping down the 11-story General Assembly Building on Capitol Square and replacing it by 2019. The plan, which also includes renovations to the Old City Hall Building next door, would cost $280 million to $300 million.

Like McDonnell’s original plan, the House version does not include any tax or fee increases.

The House budget plan includes $26 million in new funding to help hold down tuition increases at state colleges and universities.

It also includes a $144.5 million “revenue reserve fund” to offset a projected decline in tax revenues in a state long dependent on defense spending. It taps a reserve fund to fully fund the Virginia Retirement System in 2016.