WASHINGTON — House Republicans plan this week to propose more than $4 trillion in federal spending reductions over the next decade by reshaping popular programs like Medicare, the Budget Committee chairman said Sunday in opening a new front in the intensifying budget wars.

Appearing on “Fox News Sunday,” the chairman, Representative Paul D. Ryan of Wisconsin, also said Republicans would call for strict caps on all government spending that would require cuts to take effect whenever Congress exceeded those limits.

“We are going to put out a plan that gets our debt on a downward trajectory and gets us to a point of giving our next generation a debt-free nation,” Mr. Ryan said, even as he predicted that the politically charged initiatives he intended to lay out in the 2012 budget beginning Tuesday would give Democrats a “political weapon to go against us.”

“But they will have to lie and demagogue to make that a political weapon,” he said.

Republicans and Democrats remained divided over how to reach an agreement that would avert a government shutdown, which could come as early as Saturday, when a budget bill now financing the government is set to expire.