Former President Donald J. Trump on Thursday opened the door to bringing Nikki Haley into his circle, another step in what looked to be a thawing of hostilities between the two former rivals.

“Well, I think she’s going be on our team because we have a lot of the same ideas, the same thoughts,” Mr. Trump told News 12, the New York area cable outlet, one day after Ms. Haley said that she would vote for him in the November election.

That admission from Ms. Haley, his one-time United Nations ambassador-turned-bitter rival for the Republican presidential nomination, was a seemingly requisite first step toward reconciliation between the two.

In the interview after his rally in the Bronx on Wednesday, he also engaged in a rare moment of praise for Ms. Haley, calling her “a very capable person.”

During the lopsided G.O.P. primary race, which ended in March with Ms. Haley’s withdrawal, Mr. Trump and Ms. Haley exchanged frequent attacks.

Mr. Trump repeatedly called Ms. Haley “birdbrain” and insinuated that her husband, a National Guardsmen, left for a deployment in order to escape her.

Ms. Haley increasingly clapped back at Mr. Trump and his attempts to push her out of the race, referring to him in late January as “unhinged.”

Until recently, the prospects of the two making amends appeared to be uncertain, with Mr. Trump shooting down a report this month that he was considering Ms. Haley as his running mate.

Mr. Trump has enlisted several other former G.O.P. opponents in his bid to avenge his defeat in the 2020 election: Gov. Doug Burgum of North Dakota, Senator Tim Scott of South Carolina and Vivek Ramaswamy, the entrepreneur.

Mr. Trump’s “team of rivals mantra,” one made famous by Abraham Lincoln, appears to be a recognition of Ms. Haley’s potential value to his campaign, both in terms of dollars and votes.

Despite leaving the G.O.P. nominating contest more than two months ago, Ms. Haley has continued to draw significant numbers of voters in subsequent primaries, chipping away at critical support that Mr. Trump is likely to need in a close election against President Biden. In Wisconsin, she received more than 75,000 votes (nearly 13 percent of ballots cast) in this month’s Republican primary.

And then there are Ms. Haley’s connections to donors. In April, she was named the Walter P. Stern chairwoman at the Hudson Institute, a conservative think tank with a formidable list of high-dollar donors.

Jazmine Ulloa contributed reporting.