America cannot afford “a truculent child president” if it is to fulfil its global leadership role, the former US secretary of state John Kerry said on Thursday as he lambasted Donald Trump for failing to attend a key Armistice Day commemoration ceremony in Paris at the weekend.

Kerry is visiting the UK to promote his book and will be speaking at a Guardian Live event in London on Thursday night.

Speaking on BBC Radio 4’s Today programme, Kerry spoke of “a dearth of a leadership on a global basis” adding: “Every country is feeling the pressure of this nationalistic populist and in some cases very frightening rightwing advance.”

He said: “I was appalled that rain drops prevented the president from going to pay honour to those that died in rain, gas, snow and mud. That was the reason he came to Paris.”

Trump refused to attend the rain-swept ceremony citing concerns that his helicopter could not fly due to the weather, and his belief that if he travelled by car, the Paris traffic would be severely disrupted.

Kerry said: “People are tired of the embarrassment of what took place in Paris in the last few days. We cannot have a truculent child president. We need something serious.”

Despite his personal criticism of Trump, Kerry urged his party to avoid becoming so obsessed with Trump that they call for his impeachment. The Democrat-controlled House of Representatives should do whatever is appropriate, he explained, but he said: “the Democrats should not even be talking about impeachment right now. We should be talking about the alternatives that might make life better for the people in our country.”

He highlighted climate change, saying in 30 years of political activity he had “never seen evidence mounting so powerfully as it is today about the urgency of action, but it is not happening on a global basis. Scientists have just said if we do not get our act together in the next 12 years we are in for a serious catastrophe”.

He also called for a global cyber-agreement on a similar scale to the deal restricting nuclear weapons.

Speaking on the UK Brexit debate, he said: “Suffice it to say both President Obama and myself, as secretary of state, came here to Britain before the referendum and we both were remainers”. When asked if he supported a second referendum, he replied: “I said President Obama and I were, and are, remainers”.

He said the most recent midterm elections had made a powerful statement.

“We had, for the first time in history, more than 100 million people – 113 million people vote in the midterm elections. We had seven mid-governorships flip to the Democratic party, six legislatures and the largest number of Democratic Congresspeople elected since Watergate, which took place two months after Richard Nixon resigned.”

He also rebutted the often-repeated claim that wherever Trump campaigned he won, saying Trump lost in Montana, Nevada and Arizona.

He said he had not ruled out standing as the Democratic candidate for the presidency, but said he was not “actively running round” to secure the nomination, saying as many as 20 to 25 names were being bandied around in what he described as a “mish-mash”. The only specific names he mentioned were former vice president Joe Biden and the former New York mayor Michael Bloomberg, but added there was a lot of talent in the party.