But the gap could well come in below 4%, the source told Reuters on Tuesday – little changed from the 2012 figure.
Tax revenue will be higher than expected and state spending lower, with a third factor is the change that added some 7% to the country's 2012 gross domestic product, the source said.
Israel added items to GDP including more research and development investments and new categories of private spending, bringing it into line with the United States and other Western economies.
As a result, GDP growth last year was 3.4% instead of 3.2% and the budget deficit 3.9% of GDP rather than 4.2%.
That change alone will bring the deficit target this year down to 4.3% of GDP and the 2014 target to 2.75% from 3%, the source said.
'Fiscal discipline starting to make its mark'
There will be an expected extra NIS 4 billion ($1.1 billion) of tax income, partly due to the $2.05 billion sale of the remaining 20% in toolmaker Iscar to Berkshire Hathaway.
Spending will be lower than expected in view of the late implementation of the 2013 budget after its approval in July.
Together, those factors are likely to lead to a deficit of below 4% of GDP this year, the source said.
On Monday, the ministry said the deficit in the 12 months to August was 3.3% of GDP.
"Fiscal discipline is starting to make its mark," the ministry said in a statement, adding it was considering the implications of the change of the GDP's methodology.
Lapid said Israel should continue to run a tight fiscal policy to keep the deficit under control.
"These revisions increase the likelihood of decreasing taxes over the next few years but don't expect any changes in the next few months," the ministry source said.
"...If growth is higher than expected and tax revenue is higher than expected then ...tax reductions will be considered."