KABUL  - Afghanistan has made some progress in using the law to protect women against violence but many still suffer horrific abuse despite 11 years of Western intervention, a UN report showed Tuesday.The assessment, which came a day after a senior women's rights official was shot dead, opens with the tragic death of a child bride who set herself on fire after repeated beatings by her new husband and his father.When the desperate 15-year-old girl reported her case to prosecutors she was told to withdraw the complaint or face being jailed herself.In a reflection of the desperate situation of many women in the patriarchal and war-ravaged Islamic country, the report described a sharp increase in the number of reported cases of violence against women as "an encouraging development".That is because attacks still remain largely under-reported due to cultural restraints and religious beliefs, and at times because women fear for their lives, the UN's mission in Afghanistan (UNAMA) said.The report comes more than a decade after a US-led invasion ousted the notoriously brutal Taliban regime, which barred women from going to school or to work.Billions of dollars in aid have poured into Afghanistan since then and Western countries point to advances for women as an indicator of success in a long and costly war which is increasingly unpopular at home.But NATO and the US will withdraw the bulk of their 100,000 troops by the end of 2014, and there are widespread fears that the gains made by women will be eroded after their departure.Western nations have pledged to continue pumping aid into the country after 2014, warning however that it will be conditional on respect for democracy and human rights.Girls now have the right to an education and women sit in parliament. But the report shows that the belief still runs deep that women are "secondary" to men -- as the country's top religious council said in March.There have been a series of widely publicised atrocities this year, ranging from the execution before a mob of a woman accused of adultery to the beheading of another for refusing demands by her husband's family to become a prostitute.A 15-year-old had her throat slit by a suitor after his marriage proposal was rejected, while a 16-year-old was flogged 100 times in public for allegedly having an affair. The boy involved was fined.The Afghanistan Independent Human Rights Commission recorded 4,010 cases of violence against women in the seven months between March and October this year, nearly twice as many as in the previous 12 months, the report said.In 16 of Afghanistan's 34 provinces, where the UN was able to gather detailed information, just 21 percent of 470 reports of violence against women resulted in convictions.The report listed beating and cutting as the most prevalent crimes recorded under a new law on violence against women adopted in 2009.But an increase was noted in so-called honour killings, the murder of women for perceived sexual disobedience, while women continued to be imprisoned for running away from home, often to escape abuse.The report says that prosecutors refer many cases to groups of local elders, whose judgements might include a raped woman being ordered to marry her rapist."Impunity for violence against women is endemic in Afghanistan, where perpetrators of human rights abuses are rarely held to account," Amnesty International said in response to Monday's assassination of the women's rights official.The UN report recommends that the highest levels of government, including President Hamid Karzai, "publicly emphasise that promotion and protection of women's rights is an integral part and main priority of peace and reconciliation throughout Afghanistan".