MANCHESTER, Iowa — Sen. Ted Cruz hit the accelerator Monday on his run for the Republican presidential nomination, crisscrossing the state with a packed schedule of face-to-face events with voters to recapture momentum from rival front-runner Donald Trump.

Mr. Cruz delivered a strong Christian conservative message to an overflow crowd at Fireside Pub and Steakhouse in this small agricultural town in eastern Iowa, one of three stops Monday as he began a string of 28 events before the country’s leadoff nominating contest in six days.

The busy schedule aimed to outmaneuver Mr. Trump’s unconventional campaign built on massive rallies in arenas by getting back to the basics of pressing the flesh at retail campaign stops and fielding questions at intimate town hall meetings.

“He’s doing the stuff he’s got to do because Iowa is known for its retail politics,” said Republican campaign strategist Jim McLaughlin. “That’s how you get elected out there.”

The Cruz campaign also boasts one of the best organizations in Iowa of any Republican candidate, which likely will be the key if he beats Mr. Trump on caucus night next Monday.

The Cruz campaign also has rounded up endorsements to help sway any undecided voters or people who are on the fence — including from conservative TV host Glenn Beck.

Mr. Cruz picked up an endorsement Monday from former Texas Gov. Rick Perry, who backed Mr. Cruz’s GOP rival in his 2012 Senate race.

“Ted has proven that he is ready to serve as Commander in Chief on Day One,” Mr. Perry said in a statement. “He has also proven the willingness to take on the Washington Cartel and restore power and opportunity back to the people.”

It’s part of a concerted effort to close the gap in Iowa, which is viewed as a must-win for Mr. Cruz that could propel him into contention in the first primary in New Hampshire and other contests down the road.

Mr. Trump continues to lead in national polls and in every early-voting state.

In Iowa Mr. Trump topped Mr. Cruz 33 percent to 26 percent in an American Research Group poll released Monday. They were trailed by Florida Sen. Marco Rubio at 11 percent, retired neurosurgeon Ben Carson at 7 percent and Kentucky Sen. Rand Paul at 4 percent.

The other candidates finish in low single digits in the survey of likely Iowa caucusgoers.

Mr. Trump solidified his lead in recent weeks, as he attacked Mr. Cruz in TV interviews and at rallies. He has questioned Mr. Cruz’s eligibility for president because he was born in Canada, his ties to Wall Street and his opposition to ethanol subsidies.

Most recently, he accused Mr. Cruz of having a bad reputation on Capitol Hill, saying he is “nasty” and “everybody hates him.”

Mr. Cruz had attempted to beat back Mr. Trump by questioning his conservatism and his “New York values.” But lately he has backed off.

At the pub and steakhouse, Mr. Cruz said he was taking the high road. That appealed to voters known for being “Iowa nice.”

“He has recently decided to toss some insults my way. Well, I have no intention of responding in kind,” Mr. Cruz said to applause. “I think the people of Iowa deserve better and are not interested in seeing politicians bicker and throw insults and go down in the mud. So I’m not going to do it.”

He was joined at the event by Rep. Steve King, the Iowa Republican who is extremely popular with conservative and rural voters.

Mr. Cruz carefully explained his opposition to ethanol subsidies, which is a pocketbook issue in corn-producing Iowa. He said he opposed all federal energy subsidies, including for oil, wind and solar.

“That would be a level and fair playing field for everybody,” said Mr. Cruz.

He proposed eliminating the Environmental Protection Agency caps on the amount of ethanol allowed in gasoline. That would increase ethanol’s share of the market and prove more profitable for corn farmers than subsidies, he said.

He added that Mr. King wouldn’t be supporting him if he had the wrong stance on ethanol.

Mr. King nodded his approval.

Throughout the event Mr. Cruz quoted Scripture and made a forceful appeal to the state’s evangelical voters, who make up about 60 percent of GOP caucusgoers in recent years, according to exit polls.

Mr. Cruz and Mr. Trump both have heavy support among evangelicals as well as conservatives and tea party members.

The message resonated with the crowd, including with David Gould, 64, a retired state fisheries worker who pledged to caucus for Mr. Cruz.

“He’s got the values I do — solid Christian values,” he said after the meeting. “We’ve got to get back to the Constitution and get this country back on track.”

Mr. Cruz touted his record fighting and winning for conservative causes, including being pro-life and for traditional marriage, gun rights, and against amnesty for illegal immigrants.

He called each of these fights “a time for choosing” and asked voters to measure his record against his competitor.

He singled out Mr. Trump, though not mentioning his name, when talking about the fight against abortion. But he reminded the crowd that the billionaire businessman had been pro-choice for most of his life.

“If right to life matters, then ask what is your record,” said the Texas senator. “Because if you’ve got a candidate who has for 60 years of his life supported partial-birth abortion, we should not be surprised if, as president, that candidate will not defend the right to life.”

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