Mr Gingrich was challenged over his work with federal housing firm Freddie Mac, while Mr Romney had to explain his stances on gay marriage and abortion.
The two rivals played it safe, but their conservative credentials were assailed by lower-tier candidates.
The eventual nominee faces Democratic President Barack Obama next November.
Thursday night's two-hour forum, hosted by Fox News in Sioux City, Iowa, also featured Texas Republican Ron Paul, Minnesota Congresswoman Michele Bachmann, Texas Governor Rick Perry, former Utah Governor Jon Huntsman and former Pennsylvania Senator Rick Santorum.
'Scam'
In his opening remarks, Mr Gingrich challenged the president to series of lengthy policy debates: "I believe I can debate Barack Obama and I think in seven three-hour debates, Barack Obama will not have a leg to stand on in trying to defend a record that is terrible and an ideology that is radical."
Mr Romney lambasted President Obama for trying to "appease or accommodate the tyrants of the world", criticising his approach to retrieving a drone which recently went down in Iran.
"Foreign policy based on pretty please? You have to be kidding," Mr Romney said. » | Steve Kingstone, BBC News, Washington | Friday, December 16, 2011
