She is the daughter of Eitan Livni, born in Poland, and Sara Rosenberg, both of whom were members of the anti-British, Jewish terrorist organisation called Irgun.
Issuing a warrant for the arrest of an Israeli politician is one of the "biggest political mistakes the UK has ever made", Israel's president says.
President Shimon Peres said it was "high time" the British government changed a law allowing courts to grant such warrants.
The arrest warrant for Israeli former Foreign Minister Tzipi Livni has caused huge embarrassment in London.
British ministers have said they will look "urgently" at reforming the law.
UK Prime Minister Gordon Brown rang Ms Livni's office on Wednesday to tell her she would be welcome in the UK.
It is currently unclear what lasting effect the row will have on Britain's role in the Middle East peace process.
Foreign Secretary David Miliband said Israel was a "close friend" of the UK.
In a statement on Tuesday he said: "The Government is looking urgently at ways in which the UK system might be changed in order to avoid this sort of situation arising again."
One day I hope in my life time I will get the chance to see the jailers become the inmates.
Gordon Brown needs a history lesson. British Sergeant's murdered by Zionist Terrorist group Irgun.
In the early hours of the 12th of July, 1947, two British field security NCOs, Sergeants Paice and Martin, were held up by five armed members of Irgun and driven off to a secret hiding place. Three weeks later their bodies were found hanging from a eucalyptus tree...
By 1948 some 200 British Soldiers and 90 British policemen had been murdered by nationalist terrorist gangs such as Irgun...
The nationalist ‘fight’ was also extended to acts of terrorism in Britain and against British people and property in Europe.
The terrorist groups Irgun and the Stern Gang (known as Lehi in Hebrew) were active in Britain throughout the late 1940s.
It is a matter of record, for example, there were plans to crash an aircraft into the House of Commons, and to murder members of the British armed forces.
The British Embassy in Rome was bombed.
In November 1944 Lord Moyne was murdered by members of the Stern gang in Cairo and there are reliable reports of the existence of plans to assassinate Government Ministers, including the Foreign Secretary Ernest Bevan.
In 1946 a female agent of Irgun planted a bomb at the Colonial Office in London. According to Commander Leonard Burt of Special Branch this would have “blown the sort of hole that was blown in the King David Hotel”.
It was only by good fortune that a failure of the pocket-watch timer prevented detonation.
Another Irgun terrorist operating in Britain at the time was Monty Harris. Harris was sentenced to seven years imprisonment after being convicted of making thermite incendiary bombs on his premises at Gravel Street near Petticoat Lane. The use to which these devices were to be put was never established.