"There is now significant danger of such a provision being exploited by politically-motivated organisations or individuals who set out only to grab headlines," he wrote in the article published on Thursday.
Opposition to change
Human rights groups and British Muslim organisations have voiced their opposition to any change.
Benjamin Ward, deputy director of Human Rights Watch in Europe, said his organisation "would be concerned with any proposal that would effectively
abolish private prosecutions for these crimes".
The London court has issued a warrant for the arrest of Livni, who is now the leader of Israel's opposition Kadima party, over her role in Israel's 22-day war against the Hamas-rule Gaza Strip, launched at the end of 2008.
A UN fact-finding mission to Gaza last year said both Israel and Palestinian groups were guilty of war crimes and possible crimes against humanity during the war that ended on January 18, 2009 with mutual ceasefires.
Following December's spat Israel demanded the Britain change the law, which was described as "absurd" by politicians in the Jewish state.
Livni welcomed the proposed changes on Thursday, saying: "The current situation ... enables the more cynical elements to take advantage of the system.
"The warrant that was issued against me according to the legislation was an absurd use of this law," she told the newspaper.
The exact nature of the reform has not yet been made clear by the government, but parliament would have to approve the rule change before it became law.
Under the current law, heads of state and senior ministers enjoy immunity, but pro-Palestinian groups have used the principle to try to arrest former or retired Israeli officials, including Livni and retired general Doron Almog, who narrowly dodged arrest at Britain's Heathrow Airport in 2005.