The BBC's Jon Leyne in Washington says Mr Sharon is likely to come under pressure to show restraint in dealing with the Palestinians.
The US is concerned that an upsurge in violence could hinder efforts to win allies in the Arab world, and it has recently made rare criticisms of Israeli raids in the West Bank and Gaza.
Earlier, apparently under pressure from the US, Israel said it was considering withdrawing its troops from more Palestinian areas in the West Bank, reoccupied after a spate of suicide attacks.
Israeli Defence Minister Binyamin Ben-Eliezer said the pullout from the town of Hebron could be completed by the end of this week and talks were under way on the issue.
In other developments, Israeli police briefly detained Jerusalem's chief Muslim cleric, Sheikh Ikrema Sabri, in connection with allegations of incitement.
Mr Sabri, the mufti of Jerusalem, was released after several hours of questioning at a police compound over the allegations related to a newspaper article in June in which he appeared to condone suicide bombings.
Israeli police also said four people were injured on a bus in northern Israel, amid conflicting reports about the incident.
One initial report spoke of a bomb attack on the bus, near the town of Beit Shean, some 80 kilometres (50 miles) north of Jerusalem.
But police then said the bus came under attack from a gunman and launched a search of the area.
US pressure
Our correspondent says that as a possible war with Iraq approaches, President Bush has some pressing concerns with Ariel Sharon.
The US is worried about an upsurge of violence in the West Bank and Gaza, and Washington has already applied discreet pressure with a letter it sent to the Israeli Government before the weekend.
The US criticised Israel for recent civilian casualties amongst the Palestinians, and for maintaining restrictions on the Palestinian people.
"In effect, the talks could set red lines for Israeli operations in the West Bank and Gaza Strip," a security source was quoted by Reuters news agency as saying.
Our correspondent says that for his part, Mr Sharon is concerned that Palestinian groups might see the next few months as an opportunity to launch attacks with less fear of retaliation.
The US has also not received the assurance it would like that Israel will stay out of any war with Iraq, even if it is attacked.
As for the Palestinians, our correspondent says they are terrified that Mr Sharon would use the cover of a wider war to launch new military action in the West Bank and Gaza - tougher even than the events of the last few months.