WASHINGTON — President Obama will call this week for Republicans to join him in writing a broad plan to raise revenues and reduce the growth of popular entitlement programs, as the battle over the nation’s financial troubles moves past Friday’s short-term budget deal and into a wider and more consequential debate over the nation’s long-term fiscal health.

In a speech to be delivered at a university here on Wednesday, Mr. Obama will in effect come off the sidelines on the debate over reducing the nation’s debt, which is reaching dangerous heights as the population ages.

After months of criticism that he has not led on budget talks, Mr. Obama will urge bipartisan negotiations toward a multiyear debt-reduction plan that administration officials said would depart sharply from the one proposed last week by House Republicans.

The Republican plan includes a shrinking of Medicare and Medicaid and trillions of dollars in tax cuts, while sparing defense spending. Mr. Obama, by contrast, envisions a more comprehensive plan that would include tax increases for the richest taxpayers, cuts to military spending, savings in Medicare and Medicaid, and unspecified changes to Social Security.