Rivlin, a close associate of Sharon, visited Tuesday the settlement of Shiloh, 10 kilometres (six miles) north of Ramallah, to take part in the inauguration of a new neighbourhood under construction.
Sharon said in an interview on April 13 that Israel, as part of the peace process, would have to relinquish some areas closely associated with Jewish history.
"We are talking about the cradle of Jewish civilisation. Our whole history is bound up with these places. Bethlehem, Shiloh and Beit El.
"And I know we will have to part with some of these place. There will be a parting from places that are connected to the whole course of our history. As a Jew, this agonises me," he said.
His comments caused anger among the pro-settlement Israeli right-wing, which saw in them a hint that he might be willing to give up the settlements named.
Rivlin, who made only guarded comments on Sharon's words, also visited Beit El, saying he traditionally spent the Jewish festival of Passover in settlements.
"I can't imagine the prime minister wants to transfer Jews" from their homes, he told AFP.
Sharon has long been a champion of the settlement movement in the West Bank, although a new international peace plan still under wraps in Washington, and which he says he accepts "in principle," calls for a freeze in settlement growth
A crowd of around 100 settlers and their families turned out to greet the Knesset speaker in a festive atmosphere as he poured cement and laid the first brick in a show of solidarity with the settlers.
Adi Mintz of the Jewish settlers council said Sharon's words had reinforced the need for settlers to expand their communities.
"This project has been planned for a long time. Shiloh is now full up. There is a lot of demand (for housing). Sharons' words have bolstered the need to build," he told AFP.
Israeli radio said the new project involved the construction of some 30 private homes.
Jewish settlements, considered illegal by the international community, are the main focus of the 30-month Palestinian uprising, or intifada, which has left more than 3,000 people dead, mostly Palestinians but also hundreds of Israelis.
Around 200,000 people live in the settlements in the West Bank and Gaza Strip (news - web sites).
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