Indigenous Senator Jacinta Nampijinpa Price says 'lots' of Australians want her to be prime minister.

Speaking on Sky News after abandoning her bid to become deputy leader of the Liberal Party which saw Sussan Ley win the leadership ballot on Tuesday morning, Senator Price said she had broad support for the country's top job.

Asked if she would consider moving from the Senate to the lower house so she could eventually run as Prime Minister, the NT Senator was not shy in her ambition, noting: "Well, there is that".

"I know there's a lot of Australians who'd love to see that," she said.

It mirrors comments made by Nationals leader David Littleproud earlier on Tuesday, who said Senator Price's career ambitions extended beyond the Coalition's junior partner.

"The reality is that her ambitions exceed what the National Party can provide," he told ABC's AM.

"You can't be the prime minister [by being in] the National Party, I accept that."

Ms Ley, a moderate, became the first female leader of the Liberals in their 81-year history after winning the ballot 29-25 over Angus Taylor.

After Mr Taylor, a conservative, was defeated, Senator Price did not contend for the deputy leadership ballot, which was won by Queensland MP Ted O'Brien.

She said there "probably was an element" of the vote being a contest between the party's conservative and moderate factions, but said the result would lead to "robust debate" in the party room, something she argued didn't always happen under former leader Peter Dutton.

"Going forward, that provides that opportunity. I know there's probably many throughout the party room that are prepared to have a good, robust debate in our party room," Senator Price said.

The vote came only days after Senator Price defected from the National Party room.

She announced on Sunday her plans to run for Mr Taylor's deputy leader, who had welcomed her to the Liberals after her allegiance switch last week.

Asked about why Mr Taylor lost the vote, Senator Price said whilst there were probably many reasons, "I absolutely respect the outcome of what the party room decided".

"And of course, my concern is the state of the country under three more years of Labor, and I think that's where we can all say we all are on a unity ticket," she said.

On Ms Ley's leadership, Senator Price was coy, noting the new leader has "got a huge job ahead of her obviously".

"I don't envy that," she said.

"It is going to be a huge job to build from there, and I will look at what the opportunities come or don't come, but ultimately it's about ensuring that we hold Labor to account."

She added, "I will be supporting the leadership because that is what we have to do if we want to do a good job in opposition".