Boris Johnson's father has told Extinction Rebellion protesters that their work is "extremely important" - less than two days after his son labelled them "uncooperative crusties".
Stanley Johnson said the PM's remarks had been "made in humour".
Meanwhile, an extra 500 officers from across England and Wales will be sent to London to help police the climate change protests.
More than 600 arrests have been made since they began on Monday.
In April, there were 1,130 arrests during the group's 11 days of demonstrations.
Speaking at an event held by the group in Trafalgar Square in London on Wednesday, Stanley Johnson - a former Tory MEP - said: "I'm showing up here because I think what they [Extinction Rebellion] are doing is extremely important.
"From tiny acorns, big movements spring. We have been moving far too slowly on the climate change issue.
"I regard it as a tremendous compliment to be called an uncooperative crusty, that was a remark made in humour."
At a book launch on Monday, the prime minister said: "I am afraid that the security people didn't want me to come along tonight because they said the road was full of uncooperative crusties and protesters of all kinds littering the road.
"They said there was some risk that I would be egged."
However, his father insisted the Johnsons were "totally united" over the issue of climate change, saying: "I don't believe there is a single dissenting voice in the family.
"Don't forget we grew up in the country, we grew up on Exmoor, nature is in our blood.
"I don't think you need to say 'will he [Boris] listen [to the protests]'. If you listen to what he said on the steps of Downing Street that very first day, he ended with an appeal for movement on the environment and animal welfare, and that is a very, very good sign."
Further demonstrations continued into a third day on Wednesday, when hundreds of mothers joined a so-called "nurse-in" in Westminster.
Organiser Lorna Greenwood took her 16-week-old son to the event outside the Queen Elizabeth II centre, where Boris Johnson was announced as the Conservative Party leader in July.
"The reality is that our babies aren't safe because of the climate crisis," she told Radio 4's Woman's Hour.
"Babies have died, are dying and will die and this nurse-in protest is about women taking their babies to the centre of government, to the centre of power and saying these are the youngest lives who will be affected by the climate crisis."
She said most mothers would rather be at home recovering from birth and spending time with their child but "instead we'll be sitting in a cold street in October pleading for our babies lives in a society that hasn't come to terms with breastfeeding - for a lot of women this is a huge act of courage".
Another mother, Anna - who was there with her six-week-old baby - told BBC News that she had taken part because she was "frightened" for her children's future.
She said: "It really brought it home to me when my older daughter asked me when I was pregnant what's going to happen when she had a baby and I couldn't answer her - I don't know.
"I want to do everything I can to ensure she has a future."
2025year when the group aims for zero carbon emissions
298,000followers on Facebook
1,130people arrested over April's London protests
2018year the group was founded
On Tuesday, police warned activists intending to continue protesting in central London that they "must" go to Trafalgar Square or risk arrest.
The following day, Extinction Rebellion called on any arrested protesters to refuse bail conditions in an attempt to fill police cells across London.
In a message to supporters, organisers said: "By not co-operating we fill police cells for longer which means arrested individuals will be sent further and further afield."
In response, the Met Police has told BBC News it has capacity to hold about 650 people in police cells and that "contingency plans are in place, should custody suites become full".
The Home Office has confirmed that it is reviewing police powers around protests in response to Extinction Rebellion protests.
It follows a letter from Metropolitan Police Commissioner Cressida Dick after August's protests.
Extinction Rebellion activists are protesting in cities around the world, including Berlin, Paris, Amsterdam and Sydney, and are calling for urgent action on global climate and wildlife emergencies.