SRINAGAR, India, July 1 (Reuters) - India withdrew paramilitary troops on Wednesday from a tense Kashmir town where they shot dead four protesters to quell violent anti-India demonstrations in the past three days, the government said.

Baramulla town in north Kashmir, bordering Pakistan, is the first town in the disputed Himalayan region where the police will look after law and order.

A policy to gradually move in that direction in Kashmir had already been announced but it was expedited in Baranulla after the demonstrations this week, sparked by the alleged harassment of a Muslim woman by police on Monday.

Four protesters have died and scores have been injured in Baramulla and the neighbouring town of Sopore, where authorities extended a curfew for a third straight day on Wednesday.

"It has been decided to replace paramilitary deployments in Baramulla with J&K (Jammu and Kashmir) Armed Police immediately," a government statement said.

India's Home (Interior) Minister Palaniappan Chidambaram had said last month New Delhi plans to withdraw some troops from towns across the strife-torn region after a significant fall in separatist violence.

But anti-India protests have raged across the Muslim-majority Kashmir valley since bodies of two women, aged 17 and 22, who locals say were abducted, raped and killed by security forces, were found on May 29.

On Wednesday, thousands of people shouting "we want freedom" and "blood for blood" defied curfew and marched in Baramulla and Sopore, police and witnesses said.

A strike called by separatists to protest recent killings by Indian paramilitary forces closed much of Kashmir valley for the second day on Wednesday.

Angry protesters also set fire to an army ambulance and damaged police and paramilitary vehicles.

The clashes between police and protesters spread to several parts of Srinagar and north Kashmir, police said.

Security forces fighting separatist militants in Jammu and Kashmir, India's only Muslim-majority state, have been accused in the past of human rights violations, including rape and extrajudicial killings.

Authorities deny any systematic violations and say all reports are investigated and the guilty punished. (Reporting by Sheikh Mushtaq; Editing by Bappa Majumdar and Jerry Norton)

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