Meysoun al-Hashemi and her bodyguard were gunned down while driving through the Hai al-Ilam part of the city shortly after leaving her home.

The attack follows the killing of one of Mr Hashemi's brothers on 13 April.

In a separate incident, three Italian soldiers and one Romanian were killed by a bombing in southern Iraq.

The troops had been travelling on an Italian military convoy in the city of Nasiriya when it was hit by a roadside bomb attack.

In other developments:

• Newly-appointed Prime Minister Nouri Maliki visited Najaf to meet Iraq's senior Shia cleric, Ayatollah Ali al-Sistani

   

• US Secretary of State Condoleezza Rice and Defence Secretary Donald Rumsfeld expressed confidence in the new government after meeting Mr Maliki and other officials.

Women's leader

Mr Hashemi, head of the Iraqi Islamic Party and one of the country's most prominent Sunni Muslims, was elected on Saturday as part of efforts to form a unity government.

His sister worked as head of the women's affairs department for the party, which is Iraq's biggest Sunni political faction.

According to Iraqi police Ms Hashemi was being driven to work when gunmen in another car fired a hail of bullets at her car, killing both her and her bodyguard before speeding off, police say.

The TV station owned by the Iraqi Islamic Party showed pictures of the bullet-riddled four-wheel drive vehicle.

Presenters said attackers used a car to block the vehicle's route before swarming around and firing 32 shots inside, AFP news agency reported.

Another brother, Mahmoud, was shot dead whilst driving in the city just two weeks ago. Two days after that, the brother of another top Sunni politician, Saleh al-Mutlak, was abducted and killed.

Families vulnerable

There have been no claims of responsibility for any of these killings, but leaders of the anti-US insurgency, including most recently the head of al-Qaeda in Iraq, Abu Musab al-Zarqawi, have openly threatened Sunnis who take part in what they regard as a puppet government.

The BBC's Jim Muir in Baghdad says that while the politicians themselves are generally well-guarded, their families are more vulnerable.

Continued attacks indicate that there is clearly a campaign against Sunni politicians trying to take part in the government, our correspondent adds.

A spokesman for the main Sunni coalition, the Iraqi Accord Front, said Sunni politicians would not back down.

"The main purpose behind these criminal acts which targeted the political leaders... is to isolate us from the political process. I would like to make it clear that we will not go back to being marginalised and excluded," Dhafir al-Ani told the BBC.

Mr Hashemi's Iraqi Islamic Party boycotted the interim elections early last year, but it did take part in the December general elections.

As well as providing the vice-president, it is expecting to have several ministers in the government that is currently being put together, our correspondent says.