Revised growth estimates now suggest the construction industry shrank in the first quarter of 2012, but by less than previously thought.
Analysts say the revision may be enough to mean the overall economy narrowly avoided falling into recession for a second time.
The ONS is due to give official confirmation of this in June.
The revised figures show the construction sector shrank by 5% in the first three months of 2012, less than the 5.4% contraction initially reported.
The ONS gives its final estimates for growth in June, and if other parts of the economy remain unchanged, the economy as a whole would register zero growth, rather than a contraction of 0.1%.
The economy needs to register two consecutive quarters of negative growth to be in recession.
By Stephanie FlandersEconomics editor
However, the ONS may also revise the growth of other parts of the economy when it publishes its final estimates in June, such as the much larger services sector, which may offset the gains in construction.
Construction accounts for less than 7% of the UK economy, whereas the services sector makes up about three quarters of output.
Despite this, the construction sector's weakness has been blamed for dragging down economic growth.
The ONS figures showed that construction output fell again in the first three months of this year, reaching its lowest level in 15 years.
It was down 2.4% compared the last quarter of 2012. Output has fallen by nearly a fifth since the height of the construction boom in 2008.
The ONS will publish the Quarterly National Accounts on 27 June.

The ex-Germany captain, who has trained alone or with the Under-23s under new boss Jose Mourinho, was named in their 25-man Premier League squad on Friday.
The 32-year-old World Cup winner retired from international football this week after 24 goals and 121 caps.
Eighteen-year-old defender Axel Tuanzebe has been named in United's 27-man Europa League squad.
Only 21 non-"club trained" players - those who have spent three years at the club between the ages of 15 and 21 - can be named in squads for the European competition.
United could only count forwards Wayne Rooney and Jesse Lingard as "club trained" so a maximum squad of 23 could be named, along with four Under-21 players in Marcus Rashford, Luke Shaw, Timothy Fosu-Mensah and Tuanzebe.
Schweinsteiger signed a three-year deal in July 2015 but was told by Mourinho last month that it would be "very difficult" for him to play again for the club.
United begin their Europa League campaign away to Dutch club Feyenoord on 15 September. They are in Group A along with Turkey's Fenerbahce and Zorya of Ukraine.
Manchester United's Europa League squad for the 2016/2017 group stage: David de Gea, Sergio Romero, Sam Johnstone, Eric Bailly, Phil Jones, Marcos Rojo, Chris Smalling, Luke Shaw, Timothy Fosu-Mensah, Antonio Valencia, Matteo Darmian, Axel Tuanzebe, Paul Pogba, Juan Mata, Jesse Lingard, Michael Carrick, Daley Blind, Ashley Young, Ander Herrera, Henrikh Mkhitaryan, Marouane Fellaini, Morgan Schneiderlin, Memphis Depay, Zlatan Ibrahimovic, Wayne Rooney, Anthony Martial, Marcus Rashford.
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A revision by the Office for National Statistics (ONS) has cast doubt on the UK's double-dip recession last year.
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Midfielder Bastian Schweinsteiger has been left out of Manchester United's Europa League squad.