"I invite the president of Syria to come to Jerusalem and meet with the heads of the state and hold serious negotiations," Katsav said on Israel Radio on Monday.
But Syria rejected the invitation - opening the way for Israel to claim the diplomatic high ground.
"Partial solutions and media manoeuvres do not achieve peace in the region... Syria's longstanding position is to resume negotiations from where they stopped," the official Syrian Arab
News Agency (SANA) said.
The previous negotiations ended without an agreement on the future of the Israeli-occupied Golan Heights, overlooking the Sea of Galilee, Israel's biggest reservoir.
But officials have said the two sides, still technically at war, are divided only over the issue of control of a narrow strip of land at the water's edge. Israel was ruled by a centre-left government at the time.
Sharon did not mention the invitation to Syria in a later televised speech to parliament.
Earlier this month, Syria complained to the UN about a possible Israeli plan to increase the number of settlers on the Golan.
Israeli Agriculture Minister Yisrael Katz said the government had agreed to double the settlers to tighten the Jewish state's grip over the strategic plateau.
But he was later contradicted by Israel's Deputy Prime Minister Ehud Olmert who said there were no plans to expand the settlements.
Tested by opposition
He was obliged to appear in parliament to outline his political plans after the opposition collected enough signatures calling for him to do so. He was expected to primarily speak about the conflict with the Palestinians, but the opposition also quizzed him over Syria.
Yossi Alpher, an Israeli strategic analyst, told Reuters: "He really didn't say anything substantive... clearly on the Syrian issue he is trying to evade any serious discussion."
Agreement to resume the talks at the point at which they were suspended would effectively force Sharon to agree in advance to a pullout from almost all of the Golan Heights.
Syria's Bashar al-Asad (R) was
invited to talks in Jerusalem
Sharon has long opposed withdrawal from the strategic heights, seized by Israel in the 1967 Middle East war and annexed in 1981 in a move not recognised internationally.
Israel has voiced concern that Syria's peace gestures were an attempt to improve ties with Washington.
But some Israeli politicians said Israel should negotiate with a Syrian leader they regard as weakened by the US invasion of Iraq.
US Assistant Secretary of State William Burns, speaking to reporters in Cairo, said Washington supported "efforts to renew negotiations on the Syrian and other peace tracks".
Interrupted frequently by heckling from opposition left-wingers during his speech, Sharon reiterated his promise to impose "security" steps if Palestinians failed to dismantle resistance groups as required by the US-backed peace road map.
But he did not mention, as he had done in other recent speeches, his intention to dismantle some Jewish settlements on occupied territory and pull back to new "security lines" if the road map process collapsed.
Deputy Prime Minister Ehud Olmert earlier told the Jerusalem Post he estimated Sharon's plan would be implemented in the "second half of this year" if negotiations with the Palestinians did not resume.
Sharon said he would seek approval for any unilateral steps from the parliament prior to their implementation.
Sharon's omissions allowed him to avoid direct confrontation - for now - with nationalists in his coalition who oppose any territorial pullbacks or scrapping of settlements. Sharon has said such moves would cost Palestinians some of the land they seek for a state.
Palestinian cabinet minister Saib Uraiqat called Sharon's speech "an indication that the only plan he has is for the continuation of walls, occupation and settlements".
David Satterfield, a senior US diplomat, pressured Israel on Monday to stop building settlements and told the Palestinians to rein in resistance groups to revive peace talks.