A proposed change in the law to prohibit terminations in all circumstances won the backing of the Church but sparked demonstrations on Monday attended by tens of thousands of women.
Poland's minister for science and higher education, Jaroslaw Gowin, said the protests had "caused us to think and taught us humility".
The anti-abortion initiative, if enshrined in law, would mean abortions where a foetus had suffered irreparable damage, a woman's life was in danger, or the pregnancy was due to rape, would all be illegal.
The initiative, which gathered 450,000 signatures in support, is currently being analysed by a parliamentary commission, while a separate proposal to liberalise abortion laws has already been rejected in a vote by MPs.
Poland, which is predominantly Catholic and is already considered to have among the strictest abortion laws in Europe, is currently ruled by the ring-wing Law and Justice Party.
Polish women typically travel to Germany for terminations or other neighbouring countries, or they purchase abortion pills via the internet.
Some doctors refuse to perform legal abortions for moral reasons.