The G20 is failing poor and vulnerable countries by not agreeing to a climate plan that would ensure their people’s survival, leading figures at the Cop26 climate talks have said.

Leaders representing more than a billion of the people most at risk from the climate crisis told the Guardian they were “extremely concerned” and had hoped for more from the G20 summit in Rome.

They said the prospect of limiting global heating to 1.5C above pre-industrial levels, a vital threshold that scientists say is a “planetary boundary”, was slipping away as the UN conference opened in Glasgow.

Gaston Browne, the prime minister of Antigua and Barbuda and chair of the Alliance of Small Island States, which represents 39 countries, said: “From what I’ve seen it appears we are going to overshoot 1.5C. We are very concerned about that. This is a matter of survival for us.”

He blamed the influence of powerful private-sector interests for the G20’s failure to come up with better plans, and said developed countries would also suffer the consequences of climate breakdown. “We are here to save the planet, not to protect profits. There are very powerful multinational firms and lobbies … who benefit from fossil fuel subsidies.”

The G20 produced what some analysts said was significant progress in Rome, with a pledge to reach net zero emissions by around the middle of century and take action this decade to limit global heating to 1.5C, but poor countries said the promises were not accompanied by clear plans.

They urged the G20 leaders arriving in Glasgow for two days of talks with more than 100 other heads of state, which will be followed by nearly two weeks of talks among senior officials, to come up with more ambitious plans to cut greenhouse gas emissions. “I’m extremely worried, but despite the disappointment I’m still hopeful,” said Browne.

Sonam Wangdi, the chair of the Least Developed Countries group, which represents more than a billion people globally, said: “The progress is definitely not enough up to now. We are a long way from a 1.5C pathway. We need them to ramp up ambition. We have done our share, and we contributed least to the problem.”

At more than 1.5C of heating, many small islands face inundation from rising sea levels and fiercer storm surges, but Browne said developed countries were also at risk. “Many of them have coastal areas too,” he pointed out.

Steve Victor, the environment minister of Palau, said: “The G20 has lagged far behind where it must be to secure a safe future for the people of small island developing states. This is not an abstract concept or political issue for us. The threat of climate change, to us, can’t be overstated. We are now living it. The G20 makes up 80% of global emissions, they are the ones most critical for ensuring we can stay on a path to a 1.5C future.”

He said the G20 should agree to phase out coal, which it has failed to do, though it did agree to stop financing new coal development overseas. It should also halt fossil fuel subsidies, he added.

Bruce Billimon, the health minister of the Marshall Islands, said: “We live in a time in which the decisions we make will have impactful consequences in the future and coming generations, on our people’s health, wellbeing, safety and of course security.

“Already, at 1.1C, my country can feel the climate change effects, and beyond 1.5C, unquestionably, the people of the Marshall Islands and other vulnerable nations will be in peril. And the impacts will not only be felt in states like mine, but also, I believe it will be a ripple effect, thus in years to come all of the countries of the G20 as well.”

The UK said developing countries would have the opportunity on Monday to put these concerns to G20 leaders at a face-to-face meeting in Glasgow.

Officials from within the G20 felt that substantial progress had been made in Rome. “There has been a shift in the zeitgeist, recognising the need to look at the science and that we need to accelerate action in this crucial decade,” said one, adding that more progress could be expected at Cop26 on countries making moves away from coal, the dirtiest fossil fuel.

The G20 – which includes major fossil fuel producers such as Russia and Saudi Arabia that have long been hostile to climate action as well as the world’s biggest emitter, China – agreed to take action this decade on emissions, though they stopped short of pledging the 45% emissions cuts that scientists say are needed by 2030 to stick to the 1.5C limit.

Browne, however, said rich countries should aim to reach net zero by 2040 and developing countries by 2050.

Tom Burke, a co-founder of the green thinktank E3G, gave a positive assessment: “This is a shift from what they have previously said. The crucial words are on this decade. Previously they had only talked about 2050, which is too far away.

“This is an expression of a growing sense of urgency in the G20, driven by both events and science. This is a political signal that will add momentum to the cop and help in reaching agreement at cop. We were not expecting this language.”

Victor, however, said more was needed. “The message is simple. Show us your higher ambition. This decade is, perhaps, the decisive decade in history. If we fail to halve emissions by 2030, our chance to stay within the 1.5C limit will be lost, and with it the safe and secure future that the people of vulnerable countries deserve.”