Former President Donald J. Trump on Saturday invoked Vladimir V. Putin to support his case that the four criminal indictments he is facing are political payback, quoting the Russian president saying that the charges undercut the argument that the United States is an example of democracy for the world.

Mr. Trump made the comment during a campaign speech in Durham, N.H., in which he focused on pocketbook concerns of voters, hammered the state’s Republican governor, who endorsed one of his rivals, mocked his lower-polling competitors for not performing better and painted a dystopian vision of a country in “hell” under his successor, President Biden.

“Even Vladimir Putin says that Biden’s — and this is a quote — politically motivated persecution of his political rival is very good for Russia, because it shows the rottenness of the American political system, which cannot pretend to teach others about democracy,” Mr. Trump said as he railed against the 91 criminal charges he is facing, citing Mr. Putin speaking in September.

Mr. Trump added: “So, you know, we talk about democracy, but the whole world is watching the persecution of a political opponent that’s kicking his ass. It’s an amazing thing. And they’re all laughing at us.”

There is no evidence that Mr. Biden has meddled in the prosecutions of Mr. Trump, which are taking place in four different federal and state courts and cover a range of issues, including his possession of reams of classified material after he left office and his efforts to overturn his loss in the 2020 election.

And Mr. Biden’s Justice Department has twice indicted Mr. Biden’s son, Hunter, on gun possession and tax charges. But Mr. Trump has continued to claim, without evidence, that all prosecutors — even the state prosecutors in New York and Georgia — are doing his successor’s bidding.

Mr. Trump’s citation of Mr. Putin, an authoritarian strongman, came as critics have raised alarms about his potentially radical plans for a second term. Last week, Mr. Trump said he would be a dictator “on day one” of his presidency, a remark he called a joke but later doubled down on.

In bringing Mr. Putin’s words to his defense, Mr. Trump referred to one of Mr. Biden’s top adversaries as a credible observer of the U.S. political system. The U.S. intelligence community has assessed that Russian officials interfered in the 2016 election and have repeatedly tried to destabilize U.S. elections.

But suggesting that the United States is not much better than authoritarian countries, and positively invoking Mr. Putin, has been a recurring theme for Mr. Trump since he took office in 2017.

At the rally on Saturday, a relatively new slogan for his campaign — “Better Off With Trump” — was displayed on a screen over Mr. Trump’s head as he stood onstage before a packed crowd at the Whittemore Center at the University of New Hampshire. In his speech, Mr. Trump criticized Mr. Biden’s economic policies, and then broadly said the president had contributed to the degradation of Americans’ everyday lives.

“We’re going to bring our country back from hell. It’s in hell,” Mr. Trump said. He cited statistics like mortgage rates and attacked Mr. Biden’s energy policies. He also revived a widely condemned comment about immigrants “poisoning the blood of our country,” noting that immigrants are coming not just from South America but also Africa and Asia. He did not mention Europe.

Mr. Trump also cast his primary competitors, all of whom are trailing him significantly in state and national polls, as “back-stabbing establishment losers and the sellouts lagging far behind us,” and he called them “insincere RINOs” — Republicans in name only.

The former president spent considerable time ridiculing Nikki Haley, the former U.N. ambassador, over a much-vaunted “surge” that he said only manifested in comparison with lower-polling candidates. Though she is currently the highest-polling alternative to Mr. Trump in New Hampshire, edging out Gov. Ron DeSantis of Florida, surveys have consistently shown Mr. Trump with a double-digit lead in the state.

Ms. Haley was endorsed this week by New Hampshire’s popular Republican governor, Chris Sununu, a Trump critic whose support Ms. Haley’s team hopes will help attract more moderate Republicans and independent voters, who are allowed to participate in New Hampshire’s primary. Those voters are also being courted by other candidates, including former Gov. Chris Christie of New Jersey.

Mr. Trump railed against those efforts, accusing his rivals of recruiting “subversive” outsiders like “radical left Democrats” to cut into his lead.

He also blasted Mr. Sununu, calling him a “spoiled brat” who was doing a “bad job” and who had been insufficiently appreciative of Mr. Trump’s attention toward the state during his presidency.

“I gave New Hampshire everything they asked for and much more,” said Mr. Trump, who has long displayed a transactional, tit-for-tat view of governing. “And it’s hard to do that when you can’t stand the governor, right? But he’s a selfish guy.”

Saturday’s rally was Mr. Trump’s first event in New Hampshire in more than a month. The former president, who has kept a lighter campaign schedule than most of his competitors, has spent more time recently in Iowa, where his campaign is seeking a dominant victory that could encourage his rivals to drop out of the race.

His advisers see his path in New Hampshire as more predictable. The state gave him a decisive first primary victory in his effort to become the Republican presidential nominee in 2016.

Mr. Trump was to travel to Nevada, the third nominating state, later on Saturday to watch a U.F.C. fight in Las Vegas, and then for a rally in Reno on Sunday. He returns to Iowa for an event on Tuesday.

Before Mr. Trump took the stage in New Hampshire, his two top political advisers, Chris LaCivita and Susie Wiles, spoke briefly to reporters. Ms. Wiles said that Mr. Trump would increase the pace of his campaigning as January begins, and that their hope was to roll up successive victories in the first four states in order to be in a strong position accruing delegates by mid-March.

She said the criminal trials that Mr. Trump might be facing — including the federal case over his efforts to stay in power and the state case in Manhattan related to hush money payments to a porn star — present a “nightmare” for scheduling his campaign.

“I believe the goal is to take him off the field at a very critical time,” she said.