The Kadima party leader's remarks came as the country's new parliament was sworn in.
"[We will do] whatever is needed to deal with the terrorists and their dispatchers," he said.
"Today, with all its pain, is a celebration of the power of Israeli democracy which we will not allow to be derailed by anyone."
Shimon Peres, the Labour party leader and first of the 122 Knesset members sworn in, said the bombing would not stop Israel's democratic process.
"We are meeting today to show that nothing will hurt our ability or divert us from our path," he said.
Peres also reiterated that the Palestinians' Hamas-led government must renounce violence and recognise Israel's existence.
"[Hamas] does not recognise signed agreements, so what's the point of signing other agreements?" he added.
Sami Abu Zuhru, Hamas's official spokesman, had said earlier that the Tel Aviv attack was an act of self-defence in response to what he called "continued Israeli crimes against our people".
Olmert's Kadima party won 29 of the 120 seats in a March 28 election on a platform of finalising Israel's borders - with or without Palestinian agreement - and now faces forming a coalition.
He has until May 4 to present a new government line-up for parliamentary approval and confirm his position as prime minister.
Apart from Peres' Labour party and the Pensioners party, Olmert needs to secure at least another six seats to exercise a minimum majority of 61 MPs.
The ultra-Orthodox Shas and Yisrael Beitenu parties are probable coalition partners.
After the March 28 election, two-thirds of Israel's members of parliament were centrist of left-wing. The parliament had previously been dominated by the right-wing.