The ruling means that all abortions in Poland will be banned except in cases of rape and incest, or when the mother's life or health are considered to be at risk.
Justice minister Zbigniew Ziobro has said his ministry would submit a request to the labour and families ministry to begin the process of withdrawing from the treaty, known as the Istanbul Convention.
Jaroslaw Kaczynski, head of the governing Law and Justice party, and Jaroslaw Gowin, leader of a small party in the conservative coalition, announced in a joint statement that they had agreed to cancel Sunday’s vote and set a new date.
The exit poll, conducted by the research firm Ipsos, projected that Law and Justice won 43.6% of the votes.
The European Commission says a move to reduce the age at which Poland's Supreme Court judges must retire will undermine judicial independence, breaching the country's obligations under EU law.
Parliament passes a bill to change how the country's Supreme Court functions, a step critics see as an erosion of judicial independence under the populist Law and Justice party.
European Council President Donald Tusk says the questioning leave him in no doubt that he is a political target of the ruling Law and Justice party.
The ruling Law and Justice party says changes are needed to make courts more accountable but critics dub the move as unconstitutional.
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