Poland's Prime Minister Beata Szydlo has vowed to press on with judicial reforms, saying the government would not "yield to pressure from the street and from abroad".
On Monday, President Andrzej Duda had vetoed a controversial law to replace Supreme Court judges with government nominees.
It came after thousands took to the streets across Poland in protest.
Mr Duda said he made his decision after consulting legal experts and judges.
The European Commission had threatened to impose sanctions this week if the changes were not scrapped. European Council President Donald Tusk, a former Polish prime minister, had warned of a "black scenario that could ultimately lead to the marginalisation of Poland in Europe".
In a televised address, Ms Szydlo insisted that the Law and Justice (PiS) government would not back down.
"We all want to live in a fair Poland, this is why the reform of the courts is needed... Today's veto by the president has slowed down work on the reform.
"We cannot yield to pressure from the streets and abroad... We have a stable majority. We won't give in to pressure. We will realise our plan."
Why did president step in?
"As president I don't feel this law would strengthen a sense of justice," Andrzej Duda said in a statement on national television. "These laws must be amended."
He said he was vetoing two of the new laws but approving a third, which gives the justice minister the right to name the heads of Poland's lower courts.
Many were surprised, as the president is a former member of the right-wing ruling party which is pushing the legislation.
The PiS government has strongly rejected claims that the reforms are a move towards authoritarian rule and expressed disappointment at President Duda's decision.
The president had already intervened last week in an attempt to find a compromise.
He said he had discussed the reforms at the weekend, including with Zofia Romaszewska, a veteran dissident from the communist era. She was jailed during the years of martial law in the early 1980s but is now one of the president's advisers.
The activist had told Mr Duda she did not want to go back to the days when "the general prosecutor could do virtually anything".
Ms Romaszewska told Polish media it was completely out of the question for the attorney-general to take charge of the Supreme Court.
Opposition MPs also praised the role of protesters in influencing the decision.
Demonstrations have taken place in dozens of Polish cities, from Poznan and Lublin to Krakow, Gdansk and Warsaw, and there have been calls for the protests to continue.
Mr Duda warned that no change should lead to a separation of the state from society.
What's wrong with the reforms?
Poland's judicial system is widely viewed as slow and reforms are seen as necessary. "I'm absolutely a supporter of this reform, but a wise reform," said President Duda.
The three reforms give the justice minister and MPs broad powers and have prompted alarm from the US, as well as the EU.
- The first reform requires all Supreme Court judges to step down and gives the justice minister the power to decide who should stay on
- The second gives politicians control over who sits on the National Judiciary Council which nominates Supreme Court judges
- The third gives the justice minister the right to select and dismiss judges in lower courts
The president's initial compromise plan last week watered down the government's bid to push through its nominees for the National Judiciary Council, by requiring the support of another political party.
In his statement, the president said he regretted that a draft law on reforming the Supreme Court had not been handed to him before a vote in the lower house of parliament, the Sejm.
The president also took issue with the strengthened role of the justice minister, who also acts as attorney general in Poland.
What happens next?
In theory, the Polish parliament could now challenge the president's veto.
Law and Justice has a simple majority in the Sejm but needs a three-fifths majority if it decides to reject Mr Duda's decision. It could theoretically achieve that with the support of a smaller party, Kukiz'15, but that is not seen as certain.
A more likely step would be to spend the next weeks redrafting the two bills that the president has turned down and seek his approval. The protest movement has celebrated its success so far but is now pushing for the president to veto the third reform as well.
Much now depends on the man seen as the real power behind the government, PiS co-founder Jaroslaw Kaczynski.