Following an election in January, Lapid inherited a budget deficit of 4.2% of GDP in 2012. Fischer had urged slashing government spending and raising taxes to rein in the deficit, which is on track to top 4% again in 2013.
Lapid is a newcomer to politics and his Yesh Atid party, which promised to help ease the financial burden of the middle class, was the surprise of the election.
"We are taking responsible and courageous economic policy steps that will return the economy to a path of growth and help in dealing with the economic challenges we face," Lapid said.
Fischer said he supported Lapid's decision to maintain fiscal discipline, which was a key factor in the ability of the economy to succeed in the face of the global crisis.
"It is clear that implementation of this decision will require painful steps," Fischer said. "We must understand that this is necessary to protect the economy from deteriorating and for economic growth and stability in the future."
Earlier on Monday, Lapid presented the 2013-2014 budget framework to Prime Minister Benjamin Netanyahu and Fischer with an aim for a 2014 deficit target between 3% and 3.25%.
Lapid is seeking spending cuts of NIS 18 billion ($5 billion) and tax increases of NIS 5 billion as part of the 2013-2014 budget framework.
"We will pass a responsible budget, a budget that will help us to continue (economic) growth and maintain Israeli jobs," Netanyahu said.
Israeli media reported that income tax rates would be raised by one percentage point, value added tax will be increased to 18% from 17% and corporate taxes will rise to 26% from 25%. Budget cuts are expected mainly in child allowances and in defense.
Lapid's spokeswoman declined to confirm the actual details.
"There will be budget cuts and tax hikes but it is short term," Lapid told reporters without elaborating. "There is a manmade problem and we need to fix it now. In two years, every Israeli will feel different."
The budget needs to be approved by parliament by the end of July.
Israel's economy is forecast to grow 2.8% this year, excluding the start of natural gas production after 3.2% growth in 2012.