UPDATE 1-Denmark to contribute more planes to NATO after talks with Trump

(Adds details, quotes from Danish prime minister)

COPENHAGEN, Dec 4 (Reuters) - Danish Prime Minister Mette Frederiksen said her country would provide four more planes to NATO after holding "positive" talks with U.S. President Trump at an alliance summit in London on Wednesday.

"Regarding NATO, there is a wish for an additional Danish contribution on plane capacity, and we have said 'yes' to accommodate that," Frederiksen told a news briefing.

The planes would be added to NATO forces in 2020 and 2021, Frederiksen said, without specifying the type of aircraft.

Frederiksen also said she did not sense conflict between the United States and Denmark over Greenland, after she had rebuffed Trump's idea of buying the island in August.

She said Denmark, Greenland and the Faroe Islands were working to establish greater strategic cooperation in the Arctic region together with the United States, in an area where she said a stronger security focus was needed.

"There is a major power rivalry, which we are starting to see in the Arctic. We also see an increased Russian presence with submarines, and here we also need a closer cooperation," she said.

In an interview with Danish daily Berlingske published ahead of the summit on Tuesday, Frederiksen suggested increasing surveillance of the Arctic sea and airspace with radars and satellites in response to increased Russian activity there. (Reporting by Nikolaj Skydsgaard; Additional reporting by Stine Jacobsen; Editing by Angus MacSwan and Giles Elgood)