Sharon underwent a brain scan Thursday, and his doctors said he remained in critical but stable condition.
Olmert spoke to President Bush Thursday morning by telephone, his office said. It was their first conversation since Olmert assumed power last week.
A government official said Olmert may travel to Washington for talks at the White House. The official declined to be identified because a formal invitation has not yet been received. The U.S. Embassy in Tel Aviv said it had no information about the matter.
Since Sharon's stroke, Olmert has worked to project stability, holding Cabinet meetings and assuring the country that the government continues to function.
With parliamentary elections March 28, the Likud, abandoned by Sharon in November, is way behind his centrist Kadima party in the polls, so the primaries are crucial.
"We will see if Likud has decided to stake a hard claim on the hard right or really wants to give Kadima a challenge by moving back towards the center," Israeli analyst Reuven Hazan said.
Likud leader Benjamin Netanyahu opposes Sharon's plan to give up parts of the West Bank. But polls show that much of the Israeli public has abandoned the vision of a greater Israel.
Kadima's Olmert had previously been seen as an unlikely candidate for prime minister, but his calm stewardship of the Sharon health crisis has turned him into the clear front-runner.
Palestinian parliamentary elections are just two weeks away, with Islamic militants showing some muscle, reports CBS News correspondent Robert Berger.
A poll this week indicated that Hamas was narrowing the gap with the ruling Fatah party.
Under U.S. pressure, Israel has decided not to interfere in Palestinian elections, even though the Hamas is participating. Visiting Jewish Congressman Henry Waxman of California is unhappy with the U.S. position.
"Hamas should not participate in the Palestinian elections. It is a terrorist organization," Waxman said.
Hamas is behind many deadly suicide bombings, and Israel fears that it will join the Palestinian government and destroy the peace process.
Asked by Italian journalists about the possibility of Hamas' gaining power, Palestinian Prime Minister Ahmed Qureia replied, "let's see if Hamas really wins. Much will depend on the electors' participation, but also on the unity of Al Fatah, which remains Palestinians' historic guide."
Israel's Cabinet is to decide next week on whether to allow Palestinians to vote in Jerusalem in the Palestinian elections. Approval was expected, though Israel had threatened to prevent the voting in Jerusalem because Hamas was on the ballot.
"Jerusalem is part of Palestine, and these are our indisputable elections," Qureia said. "The people who will go to the polls have the right to chose the candidates they want."
As Sharon was in an a coma for the eighth day, medical experts raised new questions about whether treatment with blood thinners he received after an earlier stroke contributed to last week's massive brain hemorrhage.
Sharon remained in critical but stable condition Thursday at Jerusalem's Hadassah Hospital, where doctors continued efforts to end his sedation. The hospital said his heart rhythm was normal, and he would undergo a routine brain scan later in the day.
With Sharon apparently out of immediate danger, the rough-and-tumble Israeli political system got back down to business on Thursday.
Three Likud cabinet ministers resigned from Sharon's government Thursday, and Foreign Minister Silvan Sharon was expected to give notice at the cabinet meeting Sunday.
Meanwhile, Qureia said dialogue would continue with any future Israeli leader, according to comments published in Italian newspapers Thursday.
"It is not important to know who will be called to head Israel. We will dialogue with anyone who will be chosen by the people," Milan daily Il Giornale quoted Qureia as saying.
"If it is (acting Prime Minister Ehud) Olmert, we will deal with him. But even if Sharon should recover and go back to power, our positions wouldn't change," Qureia was quoted as saying.