Emmanuel Macron has vowed to make his style of politics more “humane”, but insisted he would press on with his project to liberalise the French economy and overhaul its welfare state despite five months of demonstrations by gilets jaunes (yellow vest) anti-government protesters.

In his first press conference in two years as president, Macron promised €5bn (£4.3bn) worth of cuts to income tax for lower and average earners as well as pension rises for the poorest and vowed no more schools or hospitals would be closed during his presidency, as he responded to protests.

The centrist politician conceded that he needed to inject more “humanity” into his style of governance but insisted he would not make changes to his pro-business programme, despite the ongoing anti-government Saturday protests by gilets jaunes, which resulted in sporadic rioting and arson in Paris and other cities.

Macron said he recognised the protesters’ “just demands” and “anger and impatience for change” and their feeling of not being taken into account by the “elites”, including the presidency, but public order must now be restored. He said although he respected the demonstrators who gathered at the start of the movement in November, he said it had “transformed progressively” and been marred by episodes of antisemitic violence, homophobia and rioting.

He said he stood by his project to liberalise the French economy, defending his controversial cuts to its wealth tax, which protestors sought to overturn. He said France was unique in Europe in not having dealt with its structural problem of mass unemployment so he would not go back on his planned “transformation” of the country.

He said: “I asked myself: ‘Should we stop everything that was done over the past two years? Did we take a wrong turn?’ I believe quite the opposite.”

Facebook Twitter Pinterest Macron held his live press conference in the ornate salle des fêtes at the Elysee Palace in Paris. Photograph: Ludovic Marin/AFP/Getty

Macron, France’s youngest modern leader, took questions from the media behind a sleek desk under hundreds of lights twinkling from chandeliers, in the Elysee palace’s salle des fêtes — a room which was recently completely refurbished in muted dove grey tones of carpet and wallpaper causing complaints from protesters that the presidency was spending tens of thousands on new carpet while others could not make ends meet.

Macron said he had listened and drawn conclusions from his unprecedented three-month voter-listening exercise, dubbed “the Great Debate” in which grievances were aired during thousands of town-hall style meetings.

French voters had said they wanted to pay less tax but wanted more public services. Macron said the “significant” tax cuts for low and average earners would be financed by cutting corporate tax breaks and reducing public spending by streamlining public services. He also said he wanted French people to work longer before retiring, but did not spell out full plans.

He promised to scrap the École nationale d’administration elite graduate training school for French civil servants and public officials. Saying the French style of governance needed to shift, Macron said he planned to make it easier for citizens to propose national referendums, and also would introduce 20% proportional representation into the lower house of parliament. A citizens’ committee, picked at random, would be included in consultations over how to approach climate policy. He also said there should be debate on migration policy every year in parliament

Macron insisted he wanted to re-install pride in “the art of being French”, saying France was “not a society of individuals” with their own demands, but a nation of citizens. He said he had seen hatred in some of the street demonstrations that marked a “regression in civic morality and education and I will fight against it with all my strength”.

Macron said he personally regretted sometimes having appeared hard and unfair, saying he was tough and demanding on himself and his government and sometimes it might have seemed he was being tough on the French people. He said his focus was now on making politics more “humane”.

The president, who was accused by protesters of making reforms in favour of the rich and big business, has seen his popularity ratings drop to around 30% from the 60% approval rating just after he beat the far-right candidate, Marine Le Pen, and was elected in 2017.

Already in December Macron had addressed the gilets jaunes by unveiling a €10bn package of tax cuts and income top-ups for the working poor and pensioners.

Ingrid Levavasseur, a gilet jaune protester said after the press conference that she acknowledged that “the expectations are so enormous that it was bound to be disappointing”.

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Macron also admitted differences with his German counterpart Angela Merkel on Brexit, trade and energy policy, saying “confrontations” and compromises were part of their relationship, but it was ultimately defined by a “culture of compromise”.

After France had stood firm on refusing to give the UK a much longer Brexit extension last month while Germany had a softer stance, Macron said: “On Brexit, we are not completely on the same page. On our ambitions for the climate and in energy, we are not completely on the same page.”

He also referred to what he described as the “incoherent” decision to begin EU trade talks with the US, backed by Merkel, despite US president Donald Trump’s climate policies. But he said the Franco-German relationship, with its “fruitful confrontations” was strong.