Prodi then delivered words to that effect. He also endorsed Israel's vision of remaining a Jewish state, which rules out an influx of Palestinian refugees.
Channel 10 television suggested that Prodi's statement on the continued Jewish identity of Israel was also at Olmert's prodding.
"You said something about a Jewish state [in the past]. I know that," Olmert is shown telling Prodi.
Olmert and Prodi aides had no immediate comment on the Channel 10 footage.
Before his Rome visit, Olmert marked a Berlin trip by seeming to confirm that Israel has the Middle East's only nuclear weapons – a reversal of a Israel's previous policy of "strategic ambiguity" on nuclear arms.
An Olmert spokeswoman denied that he had changed this policy, but opposition politicians still asked for his resignation.
Also during the Rome trip, Olmert called on other countries to co-ordinate efforts to stop Iran from building nuclear weapons.
Western governments, including the US and Britain, have expressed concern that Iran's uranium enrichment programme is being used to produce material for a nuclear weapon. Iran insists its programme is for civilian use.
Olmert hopes to convince Italy to back sanctions against Iran's nuclear programme.
He said they both agreed that "co-ordinated efforts are needed to stop Iran from becoming a nuclear power".
The trip to Rome comes as a truce in Gaza between the Israeli army and Palestinian armed factions continues to hang in the balance.
On Wednesday, a Palestinian was shot dead by the Israeli army in Gaza, the first such death since the ceasefire came into effect over three weeks ago.
Fighting in Gaza between Hamas and Fatah armed groups followed the decision of Mahmoud Abbas, the Palestinian president, to deploy Fatah security forces across the territory.
The deployment came after three young sons of a Fatah intelligence official were shot and killed on Monday.
Meanwhile, in the West Bank, where no ceasefire is in effect, two Palestinians were killed on Thursday.
Wahib Misleh, 25, was shot in the chest and arms by Israeli soldiers in the village of Kafr Al-Dik, medics and security sources said.
"Our troops searched the area and spotted a Palestinian who was about to throw a breeze-block at them from an elevated position. As they felt their lives were in danger, the soldiers opened fire, hitting the Palestinian," an Israeli army spokesman said.
Witnesses said Misleh was not among those throwing stones.
In a second killing, West Bank residents said men wearing plain clothes jumped out of an unmarked car and shot dead a man in a refugee camp in Nablus.
The residents identified the man as Mohammed Rammah, a member of the al-Aqsa Martyrs Brigade, an armed wing of Fatah.
Four other Palestinians were wounded during the raid, including a 12-year-old girl, hospital officials said.
The Israeli army had no comment but said it was checking the report.