Olivia Colman, Benedict Cumberbatch and Malala Yousafzai are among 2,000 leading activists, campaigners and public figures who have backed an open letter demanding urgent action to end extreme poverty, conquer inequality and fix the climate crisis.

Directed at the world leaders who in 2015 agreed a series of UN global goals – including tackling gender inequality, ending global warming and eradicating hunger by 2030 – the letter declares a state of emergency for people and planet.

“We need you to act faster,” the letter reads. “To find the finance. To track implementation. To unlock radical solutions.”

Nobel peace prize laureate Malala Yousafzai with Japan’s prime minister Shinzō Abe. Photograph: Franck Robichon/POOL/EPA

It continues: “We are watching you. And we will fight every day, for people, for planet. There are not just a few of us – there are millions with one voice and one question: how will you keep your promise and deliver dramatic progress towards the global goals this year?”

The letter follows last week’s warning by António Guterres, the UN secretary general, that the world was still “off track” on delivering the global goals. Although headway has been made on ending extreme poverty, “progress has been slow or even reversed” on all other global goals, a UN report found last year.

Environmentalist Jane Goodall said it was time for “those in power [to] now step up and play their part”.

“Now is the time for action if we are to achieve the global goals that world leaders have committed to. Not next year, not in five years – but now, in 2020. We all have a role to play. My global programme for young people, Roots & Shoots, is planting 5m trees in this year alone.”

Tarana Burke, the #MeToo movement founder, said the goals “build on a vision of a world in which women and girls can live free from violence, harassment and discrimination”.

“That’s why we must use these goals as a tool to hold our leaders to account and to boost all our efforts. I’m proud to stand with climate campaigners, human rights defenders, education activists today to send a clear message to leaders that these goals are all our goals. We are ready – and we are watching – for action.”

The letter was backed by a number of other actors and celebrities, including Emilia Clarke, Ryan Reynolds and Emma Watson, as well as campaign groups and charities such as Amnesty International, the International Rescue Committee, WaterAid and the YMCA.