In an exclusive interview with Reuters, Steinitz, a leading member of the weakened Likud party of hawkish Prime Minister Benjamin Netanyahu, also said there are no plans to further raise taxes in order to hit a deficit target of 3% of economic output.
Parliamentary elections last week returned Likud to the top spot in the 120-member assembly, albeit with 11 fewer seats.
One area "that we will have to make some moderate but still significant cuts is the defense budget, I assume. It is not easy but we did it in the past," Steinitz said during a stopover in New York before flying home.
Israel spends roughly 20% of its budget on defense. It has to find a way to close a NIS 14 billion ($3.8 million) deficit.
Steinitz stuck with the 3.5% gross domestic product growth target this year, rising from 3.3% in 2012. He added that it would not be a surprise if economic growth touches 4% in 2014.
The debt-to-GDP ratio is expected to decline to somewhere in the 73% range, down from 74.1% in 2011, he said.
One main reason for expecting an economic rebound is the return of cheaper natural gas to power Israel's industry as the Tamar natural gas field off the Mediterranean coast comes online in April. Egypt stopped supplying cheap gas in early 2012.
Steinitz took the positive economic message to Boca Raton, Florida, on Sunday where he spoke at a fundraising dinner for Israel Bonds. The event pulled in a single-evening record $230 million in sales to retail investors and Israel supporters, he said.
Separately, Israel's government sold $2 billion worth of 10-year and 30-year US dollar-denominated debt on Monday, albeit at moderate discounts.
Election coalition calculus
Steinitz, a former philosophy professor, was upbeat about attracting potential coalition partners and said he expects to play a role in the next government.
"It is quite probable that I will maintain the current position. But it is also possible that I will have another capacity," he said.
Netanyahu's alliance with ultra-nationalists led by former Foreign Minister Avigdor Lieberman won 31 seats in the elections.
However Yair Lapid, a former talk show host who is left-of-center, led the Yesh Atid (There is a Future) party to second place with 19 seats.
Lapid's appeal reflects frustration among secular middle-class taxpayers resentful of shouldering what they see as the burden of welfare-dependent ultra-Orthodox, or haredi, Jews exempt from military conscription.
Asked if helping trim the budget deficit will include cuts to Haredi welfare, Steinitz said: "We will consider this as well but as I said, I don't want to get into details."
He added that the haredi recognize they can no longer avoid sharing in the defense and security burden that is a right-of-passage for every other Israeli who serve in the military before heading off to higher education.
Steinitz, who has been finance minister since April 2009, said Lapid and Naftali Bennett, leader of the far-right Habayit Hayehudi party, have similar views on the economy.
These parties, Steinitz said, hold rational positions on how to deal with the economy and promote economic growth. "They understand you have to bake the cake before you can eat it," he said.
It is not clear if these parties would become members of a coalition government as Netanyahu, an obvious choice for prime minister, has not yet been asked to form a government by President Shimon Peres.
"It is difficult to say," Steinitz said of the Lapid and Bennett parties' participation. "It depends on their ability to compromise."
A new government is possible by late February or early March.
As for any haredi participation, whose long-standing role as kingmakers in coalition negotiations has been downgraded, Steinitz said he did not know if they would participate.
"It depends mainly on their ability to compromise on things that are very dear to them. I assume that if they are ready to compromise they will be in. If not they will stay out."