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.