Shadow Home Secretary Chris Grayling said this week that he was unsure whether it was necessary to change the law on universal jurisdiction.
He was speaking to two dozen members of the Reform community at the Sternberg Centre in Finchley, north west London, on Monday evening.
Audience members grilled him on how a prospective Tory administration would tackle the issue of universal jurisdiction.
Asked whether, should he become Home Secretary, he would seek to change the law, Mr Grayling said he was "entirely sympathetic" to Israeli concerns, but added that the government's indecision had left him unsure of whether there is a "tangible, real problem".
He said: "I am not convinced there's a legal problem at the moment. If it needs a change in the law I would change the law."
Britain should be a "facilitator" and "force for good" in assisting the Middle East peace process, he said.
Mr Grayling's response appeared to be at odds with other leading Conservatives, who have presented a united front on the issue, carefully managed by Conservative Friends of Israel.
Last week Shadow Business Secretary Ken Clarke and Shadow Attorney General Edward Garnier met Tzipi Livni in Israel as part of a Tory charm offensive. Mr Garnier used the occasion to say: "The Tories will change this law if this government doesn't... There is support for this from David Cameron and William Hague downwards. Our courts will not be venues for street protest."
When the warrant for Ms Livni's arrest was issued last December, Shadow Foreign Secretary William Hague said: "When the 2001 International Criminal Court Act was introduced, it was never meant by anyone in this House to obstruct normal diplomatic business, like the vital work of the Middle East peace process. Senior serving politicians, whom we need to talk to every day, were not meant to be affected."