She also said she would not make further use of the controversial mechanism that allowed her to force through the unpopular reforms without a parliamentary vote, outside of budget matters.
Borne spoke to AFP ahead of another day of action Tuesday organised by unions to protest the reforms to pensions, which include raising the retirement age from 62 to 64.
Stressing that she was open to talks with all social partners, she added: "We have to find the right path... We need to calm down."
But she also said the pensions reform would go ahead, subject to approval by the Constitutional Council, which will rule on the constitutionality of the legislation.
Opposition parties are hoping the Council will rule against the government over the reform because of the way it was forced through parliament without a vote.
Borne used Article 49.3 of the constitution, widely referred to as "the 49.3", to push the draft legislation through the National Assembly without a vote when it became clear the government could not be sure it had the votes required.
This latest recourse to the measure triggered two votes of no-confidence, one of which the government survived by only nine votes -- and sparked a furious reaction in the streets.
The protest movement against the pension reform has turned into the biggest domestic crisis of French President Emmanuel Macron's second mandate, with police and protesters clashing regularly in Paris and other cities since the reform was forced through.
Since becoming prime minister in May of last year, Borne has used the 49.3 11 times. But she stated on Sunday that from now on she would not use it outside of financial matters.
Asked about her priorities for the coming weeks, she said: "I have two objectives: to bring calm to the country in the face of these tensions, and to step up providing answers to the expectations of the French people."
Macron has tasked Borne with building a programme for the next stage of her administration, and is due to meet her and other senior members of the government on Monday.
Borne said that during the week of April 3, she would meet parliamentary groups and political parties, including those of the opposition, in a bid to open dialogue and with the aim of "appeasing the country".
But Jean-Luc Melenchon, a former presidential candidate for the hard-left France Unbowed party, called Sunday for the pension reforms to be withdrawn and for Borne to go.
Marine Le Pen, the far-right leader who challenged Macron in the 2022 elections, has also said Borne "should go or be made to resign by the president".
The government on Tuesday faces a fresh test as the unions have called a new day of action against the pension reform.
Since January, hundreds of thousands of French people have peacefully marched against the reform.
But a wave of strikes -- including one by Paris refuse collectors which has left the streets strewn with garbage -- and sometimes violent protests against the government's reform has attracted increasing attention in the international media.
The security forces have faced criticism for what critics say are their heavy-handed tactics in dealing with the protests.
The Council of Europe said Friday that peaceful protesters and journalists had to be protected from police violence and arbitrary arrest.
On Saturday, Borne and Interior Minister Gerald Darmanin both defended the police, denouncing the violence of hard-core protesters.
On Sunday, the IGPN, the internal affairs unit of the French police, said it had opened 17 investigations into incidents since the protests began on January 19.
Last week, the French authorities announced that a visit by Britain's King Charles III, which had been due to begin Sunday, had been postponed because of the current unrest.
A protester was fighting for his life on Sunday following clashes with police during a demonstration over water storage facilities in the southwestern village of Sainte-Soline.
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