Prime minister Liz Truss has told the party faithful that she will lead Britain through “stormy days” during the economic “tempest” caused by the Covid-19 crisis and Russia’s invasion of Ukraine.

The prime minister, in power for a month, sought to rally Conservative MPs behind her faltering leadership, at a party conference that has descended into acrimony, cabinet infighting and confusion.

She said she had three priorities for Britain: “Growth, growth and growth.”

Amid opinion polls showing slumping support for her government, Truss told delegates that she had fought to get where she was: “I know how it feels to have your potential dismissed by those who think they know better.”

Truss vowed to “get Britain moving”, adding to applause from fellow Tories that she refuses “to consign our great country to decline”.

The speech was disrupted by two protesters with a yellow Greenpeace flag saying: “Who voted for this?”

Truss reminded delegates about the government’s intervention to help households and businesses from rising energy bills, saying it was bigger than any similar scheme in other European countries.

The prime minister insisted that she was sticking to plans to “level up” the regions of the UK, a policy forged by her predecessor Boris Johnson.

“I know what it’s like to live somewhere which is not feeling the benefits of economic growth,” Truss said in her keynote speech on the final day of the party conference.

“I’ve seen the boarded-up shops and people with no hope turning to drugs,” she said. “We need to fund the furthest-behind first.”

But she insisted that the answer to Britain’s economic problems was “growing the economic pie so that everyone gets a slice”, by continuing to cut taxes.

Truss’s fiscal event last month, which featured £45bn of unfunded tax cuts, has prompted wild gyrations in sterling and gilt markets, but she remained unapologetic.

“Not everyone is in favour of change but everyone will benefit from the results,” she said. “The Conservative party will always be the party of low taxes.”

The prime minister might have hoped the conference would be a coronation after her election as Tory leader on September 5; instead she is struggling to get a grip on her party after days of political chaos.

The prime minister was forced on Monday to axe a plan to scrap the 45p top rate of tax by rebel Tory MPs, prompting home secretary Suella Braverman to accuse her colleagues of staging “a coup”. Kemi Badenoch, trade secretary, in turn accused Braverman of using “inflammatory language”.