"She decided because of the situation in the Middle East, it was the right decision to stay here in Washington," said State Department spokesman Sean McCormack. Rice had planned to leave Saturday.
Sharon, 77, remained in serious condition at an Israeli hospital after suffering a massive stroke on Wednesday. Sharon underwent a third brain surgery Friday morning and was expected to remain in a medically induced coma until at least Sunday.
If Sharon were to die, Rice would probably attend the funeral in Jerusalem, although McCormack did not mention that possibility.
U.S. officials have been careful not to publicly predict that Sharon will not return to power. Rice's travel decision is the clearest sign yet that U.S. officials consider his recovery unlikely.
The White House declined to speculate on how Sharon's illness could affect the peace process.
"The United States view of the Middle East is that the desire for progress and peace runs wide and deep," spokesman Trent Duffy said. "The president continues to pray for the recovery of Prime Minister Sharon."
The United States is Israel's closest ally and benefactor, with more than $2 billion in aid annually flowing to the tiny Middle East democracy.
Although the United States has no formal role as mediator, Rice and other officials play a key role in shepherding the peace process between Israel and the Palestinians. Rice visited Jerusalem and the West Bank several times in her first year as secretary.
Rice spoke by phone Friday morning with Israel's acting prime minister, Ehud Olmert, McCormack said. It was their first conversation since Sharon's health crisis.
Rice also spoke Friday to Australian Foreign Minister Alexander Downer, and the two discussed rescheduling her visit for March, the spokesman said.
In Australia, Rice had planned to participate in the first Asia Pacific Partnership on Clean Development and Climate with officials from Australia, China, India, Japan and Korea.
Energy Secretary Samuel Bodman and other U.S. officials will attend in her place, McCormack said.
In Indonesia, Rice had planned to meet with President Susilo Bambang Yudhoyono to discuss the country's democratic development, the fight against bird flu and Indonesia's recovery from the 2004 tsunami.
The United States restored military ties with Indonesia in November, ending a six-year ban on military contacts with the world's most populous Muslim nation. The ban was imposed because of human rights concerns.
U.S. officials said continuing to isolate Indonesia, which has been hit by several bombings by al-Qaida-linked terrorists in recent years, wasn't in Washington's strategic interest.