The Prime Minister claimed humanity had "pulled back a goal" against climate change in a stark contrast from his gloomy predictions just days earlier at the summit in Glasgow.
The claims came on a day in which scores of countries joined a pledge to cut their methane emissions by 30 per cent by the end of the decade.
Speaking at a press conference on Tuesday, Mr Johnson referred back to his previous claim that the world was 5-1 down at half time in a football match against climate change.
He said: "I think what you could say today after two days of talks with around 120 world leaders is that we’ve pulled back a goal or perhaps even two.
“I am cautiously optimistic. And I think we’re going to be able to take this thing to extra time, because there’s no doubt some progress has been made.
"I think we can be confident about one thing in the days ahead – the couple of weeks we've got. The clock on the doomsday clock I was talking about is still ticking, but we've got a bomb disposal team on site, and they're starting to snip the wires, I hope some of the right wires."
Mr Johnson also warned world leaders must not “think in any way that the job is done” on tackling climate change.
The Prime Minister insisted COP26 had begun to create “a sense of how actually you can deliver” on cutting carbon dioxide (CO2) targets, as set out at the Paris summit.
He explained: “I was at Paris and I remember what it was like. We had this great sense that we had agreed this thing that we were going to try and cut CO2 together.
“But it was also a slightly floaty feeling because we didn’t know how on earth we were going to do it.
“There was no road map, there was no very clear sense of how you could do it.
“I think what you’re starting to see here at COP26 in Glasgow is a sense of how actually you can deliver those cuts in CO2, but there is a long way to go.
“If there’s one thing that starts to give me confidence or optimism, it’s that we are starting to create – for the countries that find it most difficult to transition away from fossil fuels – we’re starting to create those coalitions of support to help them to move on.”
Mr Johnson also defended China’s president Xi Jinping over not coming to the summit, saying the decision was because of the pandemic.
The Prime Minister said “that doesn’t mean the Chinese are not engaging” and that “we’re seeing some signs of progress”, but he added more needed to be done.
Mr Johnson continued: “I think that we need China to make commitments. China has already made a substantial commitment in the sense that they’ve moved to net zero by the middle of the century, 2060 or before, as Xi Jinping says.
“China has fantastic power to make change in the way it runs its economy.
"They’ve committed to no new financing of overseas coal, that’s a big change already. You’re starting to see the impact of that Chinese decision to stop financing coal overseas in the whole Asia Pacific region already.”
The Prime Minister also dismissed suggestions the UK could hold a referendum on net zero.
Asked during a press conference whether the issue could be put to a vote, Mr Johnson said that although it was a “brilliant suggestion”, “I think this country has probably had enough referendums to be going on with for a while, that’s my general view on the matter”.
Ed Miliband, Labour’s shadow business secretary, said "the score that really matters is whether we cut carbon emissions by half this decade”.
"For all the Prime Minister's fantasy football, we’re still a very long way behind,” he said. “There has been some progress, but the next ten days needs to move beyond the pre-packaged announcements.”
Earlier the global methane commitment was formally launched with half of the world’s top 30 methane emitters, including the US, EU, Indonesia, Pakistan, Argentina, Mexico, Nigeria, Iraq, Vietnam and Canada joining the pledge.
Speaking at the summit, US president Joe Biden thanked those who have signed the “game-changing commitment”.
“Together we are committing to collectively reduce our methane by 30 per cent by 2030 and I think we could probably go beyond that,” he said.
“Today it’s approaching 100 countries that are signing on. That’s nearly half the global methane emissions … it’s going to make a huge difference.
“It’s one of the most potent greenhouse gases there is. It amounts to about half the warming we are experiencing today.”
European Commission president Ursula von der Leyen said she was “proud and happy and grateful that over 80 countries have signed up”.
She said: “Methane is 80 times more global warming than CO2. And today, global methane emissions grow faster than at any time in the past.
“So cutting back on methane emissions is one of the most effective things we can do to reduce near-term global warming and keep 1.5C. It is the lowest hanging fruit.”
Tuesday also saw the US climate envoy John Kerry claim he had never seen such ambition, commitment and urgency on climate talks.
He said: “We’ve already achieved an enormous amount at COP, in ambition, money, a whole bunch of new initiatives.
“Frankly, we’re a day and a half into this, and I’ve seen more energy and more commitment and more urgency than I’ve ever seen and I’ve been doing this since 1988.”