CHARLOTTE, N.C. (AP) — In an impassioned speech that rocked the Democratic National Convention, former President Bill Clinton proclaimed Wednesday night, ‘‘I know we’re coming back’’ from the worst economic mess in generations and appealed to hard-pressed Americans to support Barack Obama for a second term in the White House.

Obama strode onstage as Clinton wound up his speech, and the former president bowed. Obama pulled him into an embrace as thousands of delegates jammed into the convention hall roared their approval.

Conceding that many struggling in a slow-recovery economy don’t yet feel improvement, Clinton said circumstances are indeed getting better, ‘‘and if you’ll renew the president’s contract you will feel it.’’

To the cheers of thousands of Democrats packed into their convention hall, he said of Obama, ‘‘I want to nominate a man who is cool on the outside but who burns for America on the inside.’’

The race for the White House is a close one, and Obama’s campaign hoped Clinton’s speech would prove especially persuasive in an era of sluggish economic growth and 8.3 percent unemployment.

Clinton is exceptionally popular 12 years after he left office, particularly among white men, a group among whom Obama polls poorly.

The speech was deemed so important that convention planners delayed Obama’s formal nomination to a second term until Clinton had finished speaking. The familiar roll call of the states began well after television prime time in the eastern part of the country, and was on pace to last until well past midnight.