Pete Buttigieg is fourth in a four-strong pack clear of the Democratic presidential field, according to a new Washington Post-ABC News poll. But he thinks the final choice of who will challenge Donald Trump will be between him and Elizabeth Warren.

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In an interview to be broadcast on Showtime on Sunday, the mayor of South Bend, Indiana, said the race is “getting to be a two-way” between him and the Massachusetts senator.

“A world where we’re getting somewhere is that world,” he said, “where it’s coming down to the two of us”.

According to the Post-ABC poll, former vice-president Joe Biden leads nationally among likely primary voters, with 28% support, from Warren in second on 23%, Vermont senator Bernie Sanders on 17% and Buttigieg on 9%.

Asked on ABC’s This Week if this is really a two-way race, Buttigieg said: “Not yet, no. There is a tremendous amount of energy for a range of candidates who are extremely capable. I’m proud to be part of I think the most diverse field ever in Democratic politics and some formidable competition.

“But what I will say is there is amazing energy behind our campaign right now. We’re seeing it on the ground here in Iowa, we’re seeing it pick up in a lot of places. And I think voters are really narrowing down their choices instead of just getting to know us.”

Buttigieg has surged to second in Iowa, the first state to vote. According to the realclearpolitics.com average, Warren leads there with 22.3% from Buttigieg on 17%, Biden on 15.7% and Sanders on 15.3%.

In New Hampshire, the second state to go to the polls, Warren leads the RCP average with 25%, from Biden on 21%, Sanders on 20% and Buttigieg at 8.7%.

On Friday night in Des Moines, Iowa, the main candidates addressed the Liberty and Justice Celebration, a major party event. Speaking to ABC from the Hawkeye state on Sunday, Buttigieg was asked how he was different from Warren.

He took a swipe, saying: “I think we can deliver major, meaningful, bold changes that move this country forward in a way that galvanises an American majority instead of polarising our country further.”

“We’re going to need a president who can pick up the pieces and can bring the country together.”

On Friday, Warren unveiled a $20.5tn Medicare for All plan which duly attracted criticism from Democrats as well as attacks from Republicans and President Trump. Buttigieg has proposed “Medicare for all who want it”, meaning a plan that would not end private insurance cover. He also says he will not raise taxes on the middle class to pay for healthcare reform.

Asked about Warren’s contention that opponents of Medicare for All “are not going to win by repeating Republican talking points and by dusting off the points of view of the giant insurance companies and the giant drug companies”, Buttigieg said: “Well, the insurance companies are fighting my proposal, because they don’t want the competition.

“What is just not true is that her’s is the only solution. This ‘my way or the highway’ idea, that either you’re for kicking everybody off their private plans in four years or you’re for business as usual, it’s just not true. I’m proposing Medicare for all who want it.”

Medicare for All, he said “ could very well be the long-run destination”.

Buttigieg was also asked about his struggle to attract support from black voters, a key constituency. The New York Times reported recently that his own focus groups had indicated such problems were in part due to the fact he is gay.

Buttigieg said: “I think the biggest question on any voter’s mind when they’re sizing us candidates up and thinking about how they’re going to vote is this: how will my life be different if you’re president versus one of your competitors?”

He did not entirely dodge the question, adding pointedly: “And when we have the best answer to that question, I think a lot of prejudices and a lot of those other considerations fall away, and it comes down to vision and results.”

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Elsewhere in the Democratic race, this week saw former congressman Beto O’Rourke drop out. Other notable recent moves include the California senator Kamala Harris slashing staff in New Hampshire to focus on Iowa and Biden acceding to the formation of a Super pac, making him open to corporate funding.

In the Post-ABC poll, Harris, fellow senators Amy Klobuchar and Cory Booker, representative Tulsi Gabbard and the tech entrepreneur Andrew Yang all polled 2%. Other candidates with national name recognition, including former Obama housing secretary Julián Castro, polled even lower.

The Post-ABC poll also asked some sharp questions, given claims by opponents that Biden, 76, and Sanders, 78, may be too old to fight the Trump machine.

On the question of which leading Democrat had “the sharpest mental ability”, Warren led with 24%, from Biden at 21%, Sanders at 17% and Buttigieg at 15%. Harris, a former California attorney general, placed fifth on 7%.

Sanders recently suffered a heart attack. Poll respondents were split on whether he was healthy enough to be president, 48% saying he was and 45% saying he was not.