NEW YORK — He is the Republican Party's most powerful political weapon. Yet as the GOP fights to defend its delicate House and Senate majorities, President Trump is not welcome everywhere.

Some Republican candidates fear that the unscripted and relatively unpopular president could do more harm than good should he campaign on their behalf. Leading party strategists want Trump to focus his time and energy on a handful of Senate contests in deep-red states where Democratic incumbents are particularly vulnerable. In swing states — especially across America's suburbs, where the House majority will be decided — some would prefer that he stay away.

"I would like the president to do his job and I'll do mine," Dan David, a Republican congressional hopeful fighting to preserve a GOP-held seat in suburban Philadelphia, said when asked if he'd like Trump to visit his district.

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"I win or lose on my team's merits," David said. "I think that the president has a very, very full plate with foreign affairs and special prosecutor investigations."

This aversion to Mr. Trump is something the White House needs to take into account as it decides how best to deploy the president in the months leading up to the November midterm elections. But it's unclear how much Mr. Trump will heed strategists' guidance, or candidates' wishes, as he picks his targets.

The current White House strategy calls for Mr. Trump to focus on fundraising and campaigning in states key to control of the Senate, including Indiana, Montana, Tennessee, North Dakota, Missouri, West Virginia and Pennsylvania, according to a person familiar with the president's strategy who spoke on the condition of anonymity to discuss internal planning.

Vice President Mike Pence will be heavily involved in the Senate effort and also in House races, especially in rural areas that are more difficult for the president to reach.

Closer to Election Day, Mr. Trump is expected to shift his attention to rallies designed to bolster get-out-the-vote efforts.

Next on Mr. Trump's schedule: a trip to Tennessee later this month for a Nashville rally and a fundraiser in support of Rep. Marsha Blackburn's Senate campaign.

The White House's political team has a close relationship with most of the top Republican Senate campaigns, regularly sharing details on policy announcements and messaging. But Mr. Trump's travel decisions, so far at least, have been decided by the White House with little input from the Republican candidates on the ground.

Friends and foes alike acknowledge that in some parts of the country Trump can be extraordinarily effective by energizing his supporters. In others, his efforts have the potential to backfire by motivating Democrats or repelling skeptical independents and suburban Republicans.

"It's a matter of picking your locations very strategically," said Republican pollster Chris Wilson, who is involved in several midterm contests.

"Going to Florida, anywhere in the Central Time Zone would be a fantastic place for him to campaign," Wilson said, referring to a narrow slice of the state along the Panhandle. "I'd love to have Donald Trump in east Texas, parts of south Texas where he's still popular. Other parts of south Texas maybe not."

Florida Gov. Rick Scott, now running for the Senate, has appeared to be distancing himself from the president.

When he announced his candidacy last month, Scott would not say whether he wanted Trump to campaign on his behalf. A campaign spokesman declined to answer the same question this week.

In Missouri, Republican Senate candidate Josh Hawley has managed Trump's early visits cautiously. He did not attend the president's appearance last year, joining him this spring only at a private fundraising event.

Still, Hawley campaign manager Kyle Plotkin made clear the campaign would welcome more attention from the White House.

"We would love to have the president come back to the state," Plotkin said. "The president's agenda is popular, and people in Missouri want to see Trump and Republicans in charge."

It's much the same in Indiana, where Mr. Trump campaigned this month alongside Republican Senate nominee Mike Braun. The president insulted incumbent Democrat Sen. Joe Donnelly, calling him "Sleepin' Joe."

While the nickname confused some Republicans in the state, Missouri Republican strategist Cam Savage said the president injected a welcome dose of energy into the election.

"Air Force One makes a lot of noise when it lands," Savage said. "There isn't anything in American public life that comes close to that. If you're a candidate and you want attention, there's no better way."

Other presidents also have faced questions about their midterm strategy.

President Barack Obama was shunned by many Democrats in the 2014 midterm elections as he struggled with relatively low approval ratings. He focused his efforts on fundraising for his party and rallying black voters.

It was almost worse for President George W. Bush in the 2006 midterm elections. Eager to help his party in the weeks leading up to Election Day, Bush was relegated to appearing in Republican strongholds like Georgia and Texas in the campaign's final days.

Mr. Trump's approval ratings have ticked up in recent months, but they remain slightly below those of Bush and Obama at the same time.

There is another cause for caution with Mr. Trump: his unpredictability.

As he has proven throughout his brief political career, the president is one unscripted comment away from creating a headache for those he's trying to help. There's fear that his name-calling and aggressive anti-illegal immigrant rhetoric will turn off Hispanic voters, moderate Republicans and suburban women in key areas.

The results from Mr. Trump's early midterm efforts have been positive, said Steven Law, who heads the Senate Leadership Fund, a super PAC that expects to spend tens of millions of dollars helping Senate Republicans this year.

"Can't use him everywhere. There are risks in certain places," Law said. "But it just feels to me that you have a White House that is clearly cognizant of how to best deploy him, and he seems to be aware of that as well."

He added, "One of the concerns is whether he'll stick to script."

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Thomas reported in Washington. Associated Press writer Jonathan Lemire in New York contributed to this report.