One member of Extinction Rebellion (XR) said the meeting with Mr Gove was "less shit than I thought it would be, but only mildly", as the group expressed dismay at the lack of concrete action from ministers.
Five campaigners attended talks with the cabinet minister to outline their demands, which include declaring a national emergency on climate change and reducing greenhouse gas emissions to net zero by 2025.
Mr Gove said he shared their "high ideals" to tackle climate change but disagreed over the group's use of direct action, following large scale protests that brought the capital to a standstill.
“It was less shit than I thought it would be, but only mildly,” said activist Clare Farrell, who attended the meeting.
“I was surprised to hear a radical reflection on our economic paradigm from Michael Gove when he talked about how our model is extractive and destructive – and that we need to move to a circular model.
"And that similarly a debt based economy doesn’t do right by young people, that it is creating a huge debt for them and that it has to change.
“Unfortunately what failed to emerge was an actual way forward. I’d like to remind him that we have a 1 percent chance of hitting 1.5 degrees – that urgency wasn’t in the room.”
Youth representative Felix Ottaway O'Mahoney, 14, said: "This meeting has been very disappointing, we've set no concrete demands, he hasn't accepted any of our demands, he's avoided our demands as a whole, he isn't going to declare a national emergency.
"However, something has to be said for the fact he has recognised there is an issue."
He added: "He is going to meet us again in a month's time, which is a step forward that we will now be regularly meeting with political members.
"However, the rebellion has to continue because our demands have not been met."
Mr Gove said he had a "good conversation" with Extinction Rebellion and declared that he was open to "a higher level of ambition" for the government on reducing carbon emissions.
Speaking after the meeting, he said: "I explained to them that I’m not a fan of direct action – some of the steps they’ve taken in order to get their argument across are steps that I deprecate, but I also said that I believe that they’re motivated by high ideals I share.
He said it was vital to deliver "a wider level of public understanding" on climate change but questioned whether their timescale of reducing carbon emissions to net zero by 2025 was "achievable".
Mr Gove said he was "open minded" on the idea of citizens assemblies to oversee the changes, another central demand for Extinction Rebellion.
The group also met shadow chancellor John McDonnell earlier in the day, resulting in an invitation to address the shadow cabinet.
It comes after Jeremy Corbyn announced that the party will force a Commons vote on declaring a climate emergency on Wednesday.
The Labour leader praised the "inspiring climate activism" and said other nations would follow if parliament became the first in the world to declare a climate emergency.
Theresa May's spokesman said the government was committed to tackling climate change and accepted it needed to do more to cut emissions, despite being a world leader on the issue.
Asked whether Ms May agreed there was an environmental emergency, the spokesman added: "As the environment secretary has set out this afternoon, the most important thing is to ensure that the government acts. It's about actions, not the words we use."
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