On Thursday, in their first telephone conversation since Ariel Sharon was admitted to hospital, Olmert updated the US president on Sharon's health.
The leaders also discussed this month's Palestinian parliamentary election which is being contested by the Islamist movement Hamas, the prime minister's office said.
Olmert told Bush that Mahmoud Abbas, the Palestinian leader must "take steps against terrorism and disband the terrorist organisations because otherwise there can be no progress with an administration in which there are terrorist organisations as members".
Israel and the United States both regard Hamas, responsible for the majority of attacks during a five-year Palestinian uprising, as a terrorist organisation despite its embrace of the democratic process.
Hamas is contesting the parliamentary elections for a first time on 25 January, giving the ruling Fatah faction the first real run for its money.
A statement said: "Acting Prime Minister Olmert said that the Israeli people appreciated US President Bush's determination to fight terrorism and not compromise with it."
Abbas is under pressure to
disband armed groups
"The US president replied there can be no differentiation between kinds of terrorism and said that there can be no peace with terrorist organisations."
"He emphasised that the Palestinian Authority had to prove that it was able to act against terrorism and added that the US is working to establish democratic institutions in the PA that will advance peace and not terrorism."
Change in policy
Bush exhorted Hamas to change its policy on Israel and recognise its right to exist, while adding it was important for the Palestinian security services to be reformed, the statement continued.
At the end of their conversation, Bush asked Olmert to convey to Sharon's sons, Omri and Gilad, that he esteems their father very highly.
In the statement, Bush said, that it was "very important" that Sharon recover and "know that his friend in the US is thinking about him and is concerned for him".
Meanwhile, Shimon Peres, former Israeli prime minister, now allied with Sharon's new Kadima party, is to travel to Washington next week to hold talks with Condoleezza Rice, the US secretary of state, Israeli public radio reported.
The news of the visit emerged following a meeting between Olmert and Peres.