Livni, who heads the opposition Kadima party, had been expected to travel to London but cancelled the visit due to what her office said was a scheduling conflict.
But a statement from the Israeli foreign ministry later indicated that a British court had issued a warrant for her arrest.
At a security conference in Israel on Tuesday, Livni did not directly address the arrest warrant but defended Israel's conduct during the Gaza war, saying she "would make the same decisions all over again".
"When the state of Israel has to do the right thing, it has to be done - condemnation or no condemnation, statements or no statements, arrest warrants or no arrest warrants.
"This is the role of leadership, and as far as I’m concerned I would repeat each and every decision."
Israeli land, air and naval forces began bombarding the Gaza Strip last December, saying that it wanted to stop rocket attacks by Palestinian fighters.
More 1,400 Palestinians were killed during the offensive, according to estimates by human rights groups.
Thirteen Israelis, including 10 soldiers, died over the same time period, Israel said.
Britain's foreign office has yet to provide any details of the warrant issued by the court but has said it was looking into the incident.
"The UK is determined to do all it can to promote peace in the Middle East and to be a strategic partner of Israel," it said in a statement.
"To do this, Israel's leaders need to be able to come to the UK for talks with the British government. We are looking urgently at the implications of this case."
Barbara Serra, Al Jazeera's correspondent in London, said because Tzipi Livni is no longer a minister within the Israeli government it would be harder for her to claim diplomatic immunity from arrest.
"The fact that the application for her arrest warrant was successful opens up the very real prospect of a travel ban for Israeli politicians visiting the UK," she said.
"There's something called 'universal jurisidiction'. War crimes are considered to be so heinous that there should be no safe haven for alleged war criminals.
"So the idea is that it doesn't matter that the allged crimes happened over in Gaza, you can still try the case in England," he said.
Bill Bowring, a professor of law at the University of London, said the threat of prosecution is making international travel increasingly difficult for Israeli officials.
"This has happened before. It's under quite old legislation, under the fourth Geneva Convention of 1949," he told Al Jazeera.
"Basically what it says is that if a person anywhere in the world commits grave breaches against civilians then that person should be arrested and prosecuted wherever they turn up in the world."
After refusing to confirm whether the Palestine Solidarity Campaign was behind the arrest warrant, Sarah Colborne, the director of campaigns and operations with the PSC, told Al Jazeera: "I don't think this situation has embarrassed Britain.
"Tzipi Livni as foreign minister played a role in the Israeli government who decided to launch a war on Gaza. Therefore a judge issuing an arrest warrant is not a matter of embarrassment"
Sarah Colborne, Palestine Solidarity Campaign
"The judiciary and the government are separate, and they should be separate. And actually, the foreign office should stop trying to influence the judicial process.
"There are very clear responsibilities on the government under the fourth Geneva Convention to seek out and prosecute those who have been alleged of war crimes.
"Livni as foreign minister played a role in the Israeli government who decided to launch a war on Gaza. Therefore a judge issuing an arrest warrant is not a matter of embarrassment."
Pro-Palestinian activists have several times petitioned British courts to issue warrants against Israeli officials.
In September, activists tried to have Ehud Barak, Israel's defence minister, arrested over his role in the Gaza war.
A court denied the request on the grounds of diplomatic immunity.
A UN-sponsored report, known as the Goldstone report, has called on both Israel and the Palestinians to investigate accusations of human-rights violations committed during the conflict in the Gaza Strip.
Most of the criticism in the Goldstone report was directed towards Israel. It concluded that Israel had used disproportionate force and had deliberately targeted Gaza civilians, using them as human shields, while destroying civilian infrastructure.