Prime Minister Donald Tusk promised ahead of the 2023 election to ease abortion laws, but progress has so far been held up by conservative voices within the governing coalition.
The first bill, submitted by Tusk's party, aims to partially decriminalize abortion and helping someone obtain an abortion.
The second bill, put forward by more conservative parties, seeks to overturn a 2020 decision by the country's Supreme Court that banned abortion even when the fetus has serious deformities.
Abortion is currently legal in Poland only in cases of rape or incest, or when the mother's life or health is in danger.
The two bills are expected to be blocked by conservative President Karol Nawrocki, who could veto them. He has not yet commented on the issue.
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