We denounce vigilantism and the cowardly act that took place this morning
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Phill Kline, an opponent of Dr Tiller and a former attorney-general of the state of Kansas, said: "I am stunned by this lawless and violent act, which must be condemned and should be met with the full force of law."
President Barack Obama said he was shocked and outraged over the killing.
"However profound our differences as Americans over difficult issues such as abortion, they cannot be resolved by heinous acts of violence," Mr Obama said
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The shooting came two weeks after the president made a major speech on abortion at one of the main Catholic universities in the US.
Correspondents say the president is attempting to defuse the abortion issue - a highly emotive subject in US public life - by arguing that while it should remain legal, the government should do all it can to limit the number of unwanted pregnancies.
But members of the anti-abortion movement have been angered by the president's reversal of restrictions on federal funding for embryonic stem cell research and for family-planning groups which carry out or facilitate abortions outside the US.
Under Kansas state law, abortions later in pregnancy are legal only if two independent physicians agree that the mother could suffer irreparable harm by giving birth.
Dr Tiller's clinic is one of just three in the US to perform abortions after 21 weeks.
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