The prime minister said countries must be ready to "make the bold compromises and ambitious commitments" during the final week of the climate summit.
Discussions in Glasgow will continue, including what is needed to limit global temperature rise to 1.5°C.
Thousands of protesters gathered in cities around the world on Saturday.
About 100 climate change demonstrations were held in parts of the UK - including Glasgow, London, and Cardiff - while events also took place in Kenya, Turkey, France, Brazil, Australia, and Canada.
Glasgow's rally was the largest the city had ever seen, police said, with around 100,000 people taking part.
Police arrested 21 scientists during the march. The arrested had chained themselves and blocked a road bridge to the River Clyde.
Meanwhile, Environment Minister George Eustice - who is at the summit - has suggested in a new development that the government is considering introducing a carbon limit tax.
This would be a tax on goods - such as food, mobile phones, or cement - coming to the UK from countries that fail to meet the UK's climate action commitments.
He told BBC One's Andrew Marr Show that it would take time and ideally be multilateral.
"We're not going to export pollution," he said. "If you don't want that, you do want to consider something like a CO2 border tax."
Last week, world leaders attended the first half of COP26 and made a series of announcements, including:
Summit's first major deal, with more than 100 world leaders pledging to end and reverse deforestation by 2030
The US and EU unveil a global partnership to reduce emissions of the greenhouse gas methane by 2030. More than 100 countries have joined the initiative
More than 40 countries commit to moving away from coal
Chancellor Rishi Sunak presents plans to encourage big businesses to work towards UK net-zero 2050 target
A deal with South Africa receiving $8.5 billion (£6.2 billion) to end its dependence on coal
The parts of the Paris Agreement - the world's first comprehensive deal to tackle climate change - that remain to be finalized relate to carbon trading markets, transparency about what countries are doing, and common timetables for action.
Discussions will also continue on negotiations on financing for poor countries to adapt to a changing climate, as well as on a summit cover decision commitment. It sets out how countries will close the gap between the measures to reduce emissions they have committed to and what is needed to avoid dangerous temperature rises above 1.5°C.
The world is now about 1.2C warmer than it was in the 19th century - and extreme weather events such as heatwaves, floods, and wildfires are already intensifying. But unless more is done, the planet is already on track to warm by more than 2 degrees by the end of this century.
Several countries, as well as UN Secretary-General Antonio Guterres, want accelerated action on emissions reductions this decade to keep the 1.5C target alive.
Climate change experts and campaigners have welcomed the pledges, but argued they must be kept — and warned that an earlier deal in 2014 "hadn't slowed deforestation at all".
Similarly, activists have argued that the coal deal is "far from the required ambition" because the "fine print gives countries enormous leeway" to choose when to phase out fossil fuels.
How the world is reacting to COP26
Why we march in Glasgow
Mr. Johnson said: "There is still one week before COP26 to perform for the world, and we all need to work together and drive for the line."
He said countries have "brought ambition and action to help limit rising temperatures," and referred to commitments made at COP26 — including on deforestation and methane emissions.
"But we cannot underestimate the task ahead of us to keep 1.5C alive," he added.
“Countries must come back to the table this week to make the bold compromises and ambitious commitments needed.”
Shadow Minister Ed Miliband has warned that the world is "far away" where it is necessary to take the "great steps" to ensure global warming does not exceed 1.5°C.
The Labor MP urged the prime minister to personally lead the negotiations in the closing days of COP26, rather than engage in "empty exhortations and commentary".
He said: "We have a right to expect him to go directly into these final days, personally drive these negotiations forward, get all the major emitters to do more, provide needed funding for developing and vulnerable countries, and ensure that we have a have way out of Glasgow to keep 1.5 alive.
"He must rise with focus, clarity, and urgency in the face of the huge task ahead of the world in the coming days."
COP26 President Alok Sharma said the billions of dollars to restore the natural world promised during the first week of the summit were humanity's "first line of defense" against the crisis.
He told a news conference in Glasgow on Saturday that if the world warms 1.5°C above industrial levels, 70% of coral reefs would be lost. If it gets to 2C, they'll all die, he said.
Mr. Sharma said the UK will provide £500 million to protect more than five million hectares of tropical rainforests and create thousands of green jobs in Africa, Asia, and Latin America.
The UK is also launching a £65 million Just Rural Transition support program to help communities transition to more sustainable methods of farming and food production, he added.
You must be logged in to post a comment.