The prime minister told MPs he will visit Aberdeen on Thursday to outline further plans about what can be done to help the "vital industry at this vital time".
He later said the collapse in the oil price and taxation in the weeks after September 2014's Scottish independence referendum will not affect Scots due to the "broad shoulders of the United Kingdom".
Cameron added: "But had Scotland been independent, it would be a very, very dark day indeed."
Speaking during prime minister's questions, Conservative Peter Aldous (Waveney) told Cameron: "The North Sea oil and gas industry on which many people in my Waveney constituency are dependent for their livelihoods is facing very serious challenges at the current time.
"The government has taken steps to address the situation but more is required if the industry is first to survive and then to thrive.
"Will you assure me that you recognise the seriousness of the situation and you'll do all that you can to get the industry through these very difficult times?"
The PM replied: "You are absolutely right to raise this, I do recognise the seriousness of the situation.
"The oil price decline is the longest in 20 years and nearly the steepest and this causes real difficulties for the North Sea and we can see the effects in the east of England, across Scotland - particularly in Aberdeen - and in other parts of our country too.
"We discussed this at cabinet yesterday. I'm determined we build a bridge to the future for all those involved in the North Sea.
"We're going to help the sector export its world-class expertise. We're going to help the economies diversify. We've announced £1.3bn of support last year for the North Sea. We're implementing the Wood review.
"I'll be going to Aberdeen tomorrow where we'll be saying more about what we can do to help this vital industry at this vital time."
Cameron made his remarks on Scottish independence in response to a question from the SNP's Margaret Ferrier (Rutherglen and Hamilton West), who criticised Chancellor George Osborne for having "utterly failed to get the deficit under control".