According to a statement issued by the Kadima leader, Brown said that Livni was "most welcome" in Britain at any time and that he planned to work to change the current legal situation.
Livni clarified that there was a need to immediately repair the situation created, not for herself, "but for each and every decision maker, commander and soldier in Israel and worldwide, who are forced to fight terror."
Livni addressed the issue during her meeting Wednesday with Lithuanian Foreign Minister Vyagaudas Usackas. "Israel is dealing today with a matter which must bother every democracy in the world, and especially the NATO members – the phenomenon of abusing legal systems and filing lawsuits against Israeli officials and IDF soldiers," she said.
"This is not a new phenomenon of the past few days, and in many aspects this is not a personal lawsuit against me or against the State of Israel, but a lawsuit against every democratic country fighting terror. Those terrorists must be sued, not the people fighting against them. This is a challenge shared by the entire free world, not just Israel or Britain."
On Tuesday, British Foreign Secretary David Miliband met with Israeli Ambassador to the UK Ron Prosor, and said the British government would act with expediency to change the insufferable situation caused by the issuing of a warrant for the Opposition leader's arrest.
Miliband spoke with both Livni and Foreign Minister Avigdor Lieberman and said he and British Ministry of Public Security officials were "shocked" to learn of the warrant.
Relaying a message via the British Embassy in Israel, Miliband stressed that London sees Jerusalem as "a strategic partner and a close friend of the UK. We are determined to protect and develop these ties. Israeli leaders – like leaders from other countries - must be able to visit and have a proper dialogue with the British Government.
"The procedure by which arrest warrants can be sought and issued without any prior knowledge or advice by a prosecutor is an unusual feature of the system in England and Wales. 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," he said.
The Guardian newspaper reported Monday that a warrant for Livni's arrest had been issued by a British court, but was rescinded once it was discovered that she was not in the country. The warrant was issued following a complaint that the former foreign minister had been responsible for war crimes during the Israeli operation in Gaza about a year ago.
Livni was scheduled to travel to the UK on Sunday but canceled her trip at the last minute. The Guardian reported that the Westminster Magistrate's Court issued the warrant at the request of pro-Palestinian activists, but it was later withdrawn. The attorneys who appealed for the warrant had apparently not been informed of Livni's cancellation.