The new centrist government led by Tusk, a former European Council president, took power in December after eight years of nationalist Law and Justice (PiS) party rule. It is now trying to reverse some PiS policies, including on women's rights.
"The Istanbul Convention, the protection of women and children against violence, was inconsistent with the constitution, according to (former) Prime Minister (Mateusz) Morawiecki, Tusk said on Tuesday.
"My withdrawal of the motion means, I hope, finally putting an end to an unnecessary quarrel over this obvious convention."
In 2020 then-Justice Minister Zbigniew Ziobro asked the Labour Ministry to begin the process of taking Poland out of the treaty, saying it imposed certain ideologies on the country, and the government asked the Constitutional Tribunal to rule on it.
The Tribunal, headed by Julia Przylebska whom PiS leader Jaroslaw Kaczynski refers to as a "close friend", is one of the courts that critics say became politicised under PiS.
It ruled in 2020 that terminations of pregnancies with foetal defects should be prohibited, leading to a near-total ban on abortions. Tusk vowed to present a bill making abortion legal for up until 12 weeks, although President Andrzej Duda, a PiS ally, may veto any such law.
The Istanbul Convention, forged by the Council of Europe and dozens of member states, recognises violence against women as a violation of human rights and covers various forms of gender-based violence.
It was first signed in Istanbul in 2011 and came into force three years later. Most European Union States have signed and ratified the treaty, although the Czech Senate this year narrowly voted against ratifying it.
In 2021, Turkey itself pulled out of the treaty.
(Reporting by Pawel Florkiewicz and Anna Wlodarczak-Semczuk; Editing by Gareth Jones)
