WASHINGTON — President Obama will propose a 10-year budget on Monday that stabilizes the federal deficit but does not seek balance, instead focusing on policies to address income inequality as he adds nearly $6 trillion to the debt.

The budget — $4 trillion for the 2016 fiscal year — would hit corporations that park profits overseas, raise taxes on the richest of the rich and increase the incomes of the middle class through new spending and tax credits. Mr. Obama will challenge the newly elected Republican Congress to answer his emphasis on wage stagnation, according to congressional aides briefed on the details.

The central question that Mr. Obama’s budget will pose to Congress is this: Should Washington worry about what may be the defining economic issue of the era — the widening gap between the rich and everyone else — or should policy makers primarily seek to address a mountain of debt that the White House hopes to control but only marginally reduce as a share of the economy?

The president’s budget, thicker than a phone book in multiple volumes, will be just the starting point for that discussion with Congress, representing his aspirations, not the final word. Criticism of Mr. Obama’s intentions arrived even before the budget was presented.