Gordon Brown called Ms Livni to say she was welcome in the UK
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.
The warrant was granted by a London court at the request of Palestinian plaintiffs, provoking Israeli anger.
It was revoked on Monday when it was found Ms Livni was not visiting the UK.
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."
Pro-Palestinian campaigners have tried several times to have Israeli officials arrested under the principle of universal jurisdiction, which holds that some alleged crimes are so grave that they can be tried anywhere, regardless of where the offences were committed.
Ms Livni was foreign minister during Israel's Gaza assault last winter.
She said the court had been "abused" by the Palestinian plaintiffs who requested the warrant at Westminster Magistrates' Court.
UK ambassador rebuked
It was the first time a UK court had issued a warrant for the arrest of a former Israeli minister.
"What needs to be put on trial here is the abuse of the British legal system," Ms Livni told the BBC.
PREVIOUS ATTEMPTS TO ARREST ISRAELI OFFICIALS
Oct 2009: Former military chief Moshe Yaalon cancelled a UK visit because of fears of arrest for alleged war crimes
Oct 2009: Filed attempt to raise warrant against Defence Minister Ehud Barak. Court ruled he had diplomatic immunity
Sept 2005: Arrest warrant issued for a former head of Israeli forces in the Gaza Strip, Gen Doron Almog. He received warning before disembarking from an aircraft at Heathrow Airport, and flew back to Israel
"This is not a suit against Tzipi Livni, this is not a lawsuit against Israel. This is a lawsuit against any democracy that fights terror."
She stood by her decisions during the three-week Gaza offensive which began in December last year, she said.
Israel's foreign ministry summoned the UK's ambassador to Israel to deliver a rebuke over the warrant.
Israel denies claims by human rights groups and the UN investigator Richard Goldstone that its forces committed war crimes during the operation, which it said was aimed at ending Palestinian rocket fire at its southern towns.
The Palestinian militant group Hamas has also been accused of committing war crimes during the conflict.
Israel says it fully complies with international law, which it says it interprets in line with other Western countries such as the US and UK.
Palestinians and human rights groups say more than 1,400 people were killed during Israel's Cast Lead operation between 27 December 2008 and 16 January 2009, more than half of them civilians.
Israel puts the number of deaths at 1,166 - fewer than 300 of them civilians. Three Israeli civilians and 10 Israeli soldiers were also killed.