WARSAW, March 28 (Reuters) - Thousands of demonstrators marched through Warsaw on Wednesday to demand Poland toughen its already strict abortion laws, pressing a case that has split the ruling conservative coalition government.

Police said 3,000 protesters from across the overwhelmingly Roman Catholic country attended the rally, calling for a change in the law to make it a crime to terminate a pregnancy even when a woman has been raped or her life is in danger.

The demonstration organised by the ultra-nationalist League of Polish Families, a minority party in the ruling coalition, and a fringe Catholic group, followed a decision by the European Court of Human Rights last week in favour of a Polish woman who nearly went blind after being denied an abortion.

The League and Catholic groups have called on the Polish government to fight the Strasbourg court's ruling and its decision to award compensation to the woman, saying abortion should be banned under any circumstances.

But the dominant conservative Law and Justice party has accepted the decision, opening up a split within the coalition.

Sociologist Marek Migalski at the University of Silesia said the turnout at the demonstration could be seen as a success for the organisers. A counter rally by supporters of women's groups arguing for more liberal abortion rules only drew around 1,000 in Warsaw on Wednesday, he said.

Poland has some of the toughest abortion laws in Europe. It allows a pregnancy to be interrupted only when it threatens the life or health of the mother, when the baby is likely to be permanently handicapped or when it originates from rape.

The League, which opposed Poland's European Union membership and has been accused of anti-Semitism by its opponents, wants even those exceptions closed and is pushing to change the constitution to this effect.

Prime Minister Jaroslaw Kaczynski's Law and Justice party has agreed to change the constitution to bolster the protection of unborn children but without making abortion rules tougher.

Police said both demonstrations were peaceful.

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