WARSAW (Reuters) -Poland holds a presidential election run-off on Sunday, with the ruling party's candidate, liberal Warsaw mayor Rafal Trzaskowski, facing nationalist Karol Nawrocki, in a vote crucial for the country's pro-European course.

Prime Minister Donald Tusk swept to power in 2023 with a broad alliance of leftist and centrist parties, on a promise to undo changes made by the nationalist Law and Justice (PiS) government that the European Union said had undermined democracy and women's and minority rights.

However, reforms have been slow, mainly because - the government contends - Poland's outgoing president, Andrzej Duda, a PiS ally, has been vetoing bills.

Below are the key issues at stake in the presidential contest.

SOCIAL ISSUES

Tusk won the 2023 parliamentary vote partly on promises to end a near-total ban on abortion introduced by the socially conservative PiS government.

Tusk and the Left promised to allow abortion on demand until 12 weeks and restore the right to termination in case of foetal abnormalities, but the coalition was unable to agree on a bill. It also argued that Duda would veto any liberalisation.

Nawrocki has said he would not sign any bill liberalising the right to abortion, even in the case of foetal abnormalities.

Trzaskowski has promised to fight for women's rights and to back a bill that would liberalise "this medieval abortion law".

Trzaskowski is also in favour of a bill on same-sex unions while Nawrocki has said he would not sign such legislation.

Seeking to lure voters both from the Left as well as pro-market liberals, Trzaskowski has vowed to support affordable housing initiatives while getting rid of red tape for small businesses on the other.

RULE OF LAW

During its two terms in government from 2015 to 2023, PiS introduced a series of judicial reforms which Brussels said undermined the rule of law and critics blamed for chaos in the judiciary.

The European Union's top court ruled that a new procedure for appointing judges did not guarantee their impartiality, opening the way for their rulings to be questioned.

The Constitutional Tribunal issued rulings stating that Poland's constitution had primacy over EU law, undermining a key principle of the Union. Brussels took Poland to court over the ruling, and the current government does not recognise it.

However, Tusk's efforts to roll back the changes have so far failed, blocked by Duda who keeps appointing judges under PiS rules.

Nawrocki has signalled he supports PiS's changes, suggesting that the deadlock would continue if he wins, while Trzaskowski would support the government's efforts to reverse them.

Duda also blocked the government's efforts to bring PiS politicians to justice, pardoning two members of the former government sentenced for abuse of power in their previous roles.

Critics have said Nawrocki could come under pressure from PiS to pardon its politicians. Trzaskowski said he would not pardon any politicians convicted of wrongdoing.

UKRAINE

While Nawrocki supports giving military aid to help Ukraine fend off Russia's invasion, he is opposed to Kyiv joining Western alliances such as NATO.

Nawrocki rejects suggestions that his stance is pro-Russian, while also saying that Poland has the right to raise sensitive issues with Kyiv such as exhumations of the remains of Polish victims killed by Ukrainian nationalists during World War Two.

Trzaskowski says it is in Poland's own interests that Ukraine becomes a NATO member.

EUROPEAN UNION

Nawrocki vows to resist what he sees as efforts by Tusk and Trzaskowski to promote a European super-state, cede Polish national prerogatives to Brussels and undermine the country's security relationship with the United States.

Trzaskowski says his strongly pro-EU stance will boost Poland's influence in Brussels and that this will translate into benefits including more funds for Polish security.

Both candidates support the Trump administration's demand for Europeans to spend much more on defence - Poland spends almost 5% of national output on defence, the highest level in NATO - but Nawrocki prioritises closer security ties with the U.S., while Trzaskowski favours a greater European focus.

AFTER THE ELECTION

A win on Sunday for Nawrocki would undermine Tusk's political project and could be a prelude to the return of PiS to power in 2027 or even earlier if the ruling centrist coalition crumbles and a snap election is held.

Victory for Trzaskowski would mean Tusk's coalition has an ally in the presidential palace, enabling it to streamline key legislation and also to move forward on some foreign policy issues, including nominating new ambassadors.

Regardless of the outcome, Tusk has said he wants to renegotiate the coalition agreement and reshuffle his team after the presidential election to make it leaner and more efficient.

(Reporting by Anna Wlodarczak-Semczuk and Marek StrzeleckiEditing by Gareth Jones)