Mr Dudley's comments came after BP revealed its fourth quarter profits were down one-fifth on last year at $4 billion (£2.5bn) as the scaling back of its asset base led to a 7% fall in oil and gas output in the quarter.
The earnings performance, which translated into a 18.6% drop in underlying profit to $17.6bn for the full calendar year, still beat market expectations due to the impact of taxes.
At the end of November, BP sold its interests in several central North Sea oil and gas fields to Abu Dhabi's state-owned energy company, Taqa, for more than $1 billion.
In December, Perth-based utility SSE bought BP's 50% interest in the Sean Gas field to for $288 million.
Mr Dudley said: "I imagine some people believe we are backing away from our investments in the North Sea."
But he said BP has plans to invest £10bn in UK oil projects up to 2015.
He said: "We have a focused set of assets in the North Sea. We are continuing to upgrade and bring on some new assets."
Devenick and Kinnoull in the UK North Sea are expected to be brought onstream by the end of 2014.
The company has also committed to invest in the Schiehallion redevelopment and Clair Ridge projects off Shetland.
Mr Dudley said that the UK should exploit the potential for controversial shale oil and gas exploitation which he said has "transformed" the energy market in the United States where gas prices have plunged.
"It seems natural to me the country would try to unlock what would be low cost resources," he said.
He said BP would not rule out getting involved in the UK shale industry.
In December, the UK Government announced it is lifting its temporary ban on fracking, blamed last year for triggering earthquakes near the Blackpool area.
Fracking is controversial because it involves high-pressure liquids being used to split rock and extract gas.
In the US, some fracking has been associated with the pollution of ground water and escapes of methane.
Green groups worry that large parts of Scotland could be used for fracking.
The sale of the North Sea sites were among $37.8bn worth of assets sold by BP since the Macondo spill in the Gulf of Mexico, which killed 11 men and leaked five million barrels of crude into the sea in 2010.
BP has taken a total charge against profits of $42.2bn, but has paid out most of this in compensation and fines.
BP could face making more pay-outs this year via a settlement with US authorities, or as a result of a civil penalties trial that is due to begin on February 25.
Scots Kenneth Whiteside and Carson Bilsland, were among 37 foreign workers and one Algerian killed after Islamist militants, thought to be linked to al Qaeda, seized control of the BP gas plant at In Amenas in Algeria last month.
Mr Dudley said BP is reviewing security at its plants in North Africa and beyond, and working with others in the industry on the issue.
"I do not want to overreact," he said, to what were "complex events".
Mr Dudley added that it is "too early to say" if unrest in Mali or the change of Government in Libya have "changed the dynamics" for multi-national companies in the region.
BP's shares closed up 6.65p, or 1.4%, at 468.7p..