WASHINGTON — A victorious Mitt Romney and runner-up Rick Santorum both claimed satisfaction from the close Michigan primary on Wednesday as they swiftly shifted their duel for the Republican presidential nomination to Ohio and the rest of next week’s delegate-rich Super Tuesday contests.

Campaigning in Bexley, Ohio, Romney promised “more jobs, less debt and a smaller government” if he wins the nomination and defeats President Obama in the fall. “Interestingly, the people who said that the economy and jobs were their No. 1 issue, they voted for me, overwhelmingly” in the Michigan primary, he said.

Santorum saw the events of the previous 24 hours differently, having won half of the 30 delegates in his rival’s home state primary even though he lost the popular vote.

“We had a much better night in Michigan than maybe was first reported,” he said in Tennessee.

While Santorum contended the race to pick an opponent for Obama was down to two men, Newt Gingrich and Ron Paul had other ideas as they set their own priorities for the 10 Super Tuesday contests.

That made Washington’s caucuses on Saturday something of a campaign way-station, worth 40 delegates but squeezed in between two big primary nights.

The pattern of the candidates’ schedules underscored a shift in the nature of the race, away from one-or-two-state nights where political momentum counted for much, and into a period of multiple contests, where the object is to pile up delegates in pursuit of the 1,144 needed to win the nomination at the party convention this summer in Tampa, Fla.

It appeared Romney’s narrow home state triumph after a string of weak performances had quelled talk of a late entrance into the race by another contender.

There seemed no doubt that the next major clash would occur in Ohio, a big industrial state with 8.1 percent unemployment, 63 convention delegates at stake and a long history as a battleground in general election campaigns.

Romney and Santorum have already campaigned there, and television advertising has topped $4 million in the state, a total that includes not only the two leading contenders but also super PACs that support them and Gingrich.

In a renewed commitment, the super PAC supporting Gingrich also disclosed it would spend more than $800,000 in radio ads in upcoming primary states, including Ohio, Oklahoma and Tennessee.

Santorum has been running a shoestring campaign, but a spokesman, Hogan Gidley, said the former Pennsylvania senator raised $9 million in February for his candidacy.

Romney is all but assured of victories in at least two of next Tuesday’s states — Massachusetts, where he was governor and faces little or no competition in the primary, and Virginia, where neither Gingrich nor Santorum qualified for the ballot.

Those two contests offer 84 delegates combined.

Gingrich looked to Georgia, where he launched his political career 30 years ago, to ignite an improbable comeback. The former House speaker conceded it was a state he must win, and he predicted he would, decisively. Polls show him leading, but below the 50 percent level he would need to sweep all 76 delegates.

Surveys show Santorum running strongly in Oklahoma, which has 40 delegates, while Tennessee, with 55, shapes up as a struggle. There are modest amounts of television advertising in both states, indicating several camps view them as competitive.

Paul appears to be contesting Romney in Vermont, with 17 delegates.

So far, 290 delegates have been awarded, while 419 are on the ballot next Tuesday alone. In an Associated Press tally, Romney now has 167 delegates, Santorum 87, Gingrich 32 and Paul 19.

Romney’s remark about winning the votes of Michigan primary-goers who said the economy and jobs were their top priority was grounded in exit polls, which showed he defeated Santorum among that group, 47 percent to 30 percent.