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Senator Ted Cruz’s supporters are mounting an effort to seize control of the Republican platform and the rules governing the party’s July convention, the first indication that Mr. Cruz will not simply hand his delegates over to Donald J. Trump.

In an email sent Sunday to pro-Cruz convention delegates, a top aide to the Texas senator wrote that it was “still possible to advance a conservative agenda at the convention.”

“To do that, it is imperative that we fill the Rules and Platform Committees with strong conservative voices like yours,” wrote Ken Cuccinelli, who was the campaign’s former delegate wrangler and a former attorney general of Virginia. “That means you need to come to the national convention and support others in coming, too!”

Mr. Cruz is planning a Monday evening conference call where, as Mr. Cuccinelli writes, Mr. Cruz’s former officials plan to “discuss what we can do at the convention to protect against liberal changes to our platform, and how we can right the wrongs in the rules from 2012!”

The “wrongs” Mr. Cuccinelli was referring to are the changes pushed through at the last convention by supporters of Mitt Romney that would have made it harder for a candidate’s name to be placed in nomination.

But Mr. Cruz’s supporters and other conservative activists are also deeply concerned about Mr. Trump’s general election agenda, and want to ensure that he does not alter the party’s platform. Since locking up the nomination last week, Mr. Trump has made clear he intends to run a populist campaign against Hillary Clinton, the presumptive Democratic nominee, indicating he is open to higher taxes and an increase in the minimum wage.

The party’s convention rules and policy platform are determined every four years by temporary committees comprised of a select group of convention delegates. The rules and platform are then ratified or rejected by all the delegates at the convention.

With the assumption that the party’s nomination would not be decided on the first convention ballot, Mr. Cruz spent considerable time this spring electing delegates favorable to him to the July convention in Cleveland. So while he is out of the race, many of his supporters will still be delegates. And while many convention delegates are bound to support Mr. Trump on the first ballot, they are free to vote their conscience on matters relating to convention rules and the platform.

The email, which carries the “Cruz-Fiorina” logo, was forwarded to The New York Times by a convention delegate.

Reached by telephone, Mr. Cuccinelli authenticated the message. As for Mr. Trump’s rhetorical shifts in recent days, he said, “nothing I’ve seen since a week ago has been surprising to me.”

But Mr. Cuccinelli said Mr. Cruz, who has been silent since withdrawing from the race last Tuesday, had no intention of trying to rewrite convention rules in an effort to deny Mr. Trump the nomination.

“It’s important that this not appear as though we are pulling a stunt at this convention,” he said, adding that the goal is to advocate for policies preferred by the sort of hard-line conservatives who backed Mr. Cruz’s campaign.

“This is about protecting movement conservatism,” he said, pointing to party planks on abortion and saying the delegates should consider language regarding transgender bathroom access.

“We want to have girls go in girls’ bathrooms,” he said, highlighting an issue on which Mr. Trump has broken with social conservatives by supporting the rights of transgender people to use the bathroom of their choice.

A top adviser to Mr. Trump, Paul Manafort, downplayed Mr. Cruz’s effort to take control of the convention panels.

“If there wasn’t interest and activity around the platform that would be a surprise,” said Mr. Manafort, noting that debate around the party’s policies is almost always a feature of Republican conventions. He said they would work with “the various campaigns” to find consensus on the platform.

Mr. Cuccinelli’s plea to the delegates comes as Mr. Cruz’s own supporters appear divided over whether to get behind Mr. Trump. Some of his most forceful backers – such as Rick Perry, the former Texas governor, and the pollster Kellyanne Conway, who ran a pro-Cruz super PAC – have come out for the presumptive nominee they spent months deriding. But some of Mr. Cruz’s top aides remain bitter about a campaign that saw Mr. Trump mock the senator’s wife and float conspiracy theories about his father.

Even if Mr. Cruz had not intervened, platform-related tension between Mr. Trump and social conservatives was likely inevitable. Many Christian conservatives harbor deep suspicions about Mr. Trump’s true beliefs and how compatible they are with the long-held, hard-line stances espoused in the platform.

His supportive comments about aspects of Planned Parenthood’s work and his previous support for abortion rights are among the red flags that were been making social conservatives nervous, even before he professed support for letting transgender people use whichever bathroom they choose.

Tony Perkins, one of the platform committee members from Louisiana and the president of the influential Family Research Council, said that delegates like him will need to feel more reassured than they do now.

“One of the things that’s going to be required for people like me to be supportive of his candidacy is the platform,” Mr. Perkins said, insisting that he and others on the committee who would have preferred to see Mr. Cruz become the nominee will not tolerate any watering down in the language.

Mr. Perkins said that the platform is one way that Cruz delegates hope to still exert influence, despite having lost the battle for the nomination.

“This is where the Cruz factor comes in,” he said. “Ted Cruz has been vigilant and methodical in selecting and identifying conservative delegates who are not aligned with the party, per se, but aligned with the conservative ideology. And those are the people who will be at the convention and will be on the important committees.”

Jeremy W. Peters and Matt Flegenheimer contributed reporting.

