(Updates with talks continuing, new quotes)

KAMPALA, Dec 14 (Reuters) - Senior diplomats from Uganda and the Democratic Republic of Congo were still in talks in Kampala on Friday to thrash out an agreement over their disputed border straddling an oil exploration hotspot.

"We want to harmonise relations," said Bundi Bukaka, an official with the Congolese trade ministry.

"Just like brothers, we fight. But that doesn't mean we stop being brothers."

A string of shootouts between the two former enemies on Lake Albert since August has killed a number of civilians, including a British contractor doing a seismic survey for Heritage Oil Corp. <HOC.TO>

Congolese Foreign Minister Mbusa Nyamwisi and his Ugandan counterpart Sam Kutesa are leading the talks, which have focused both on the border dispute and a review of a 1990 oil exploration agreement.

Besides Heritage, Tullow Oil <TLW.L> is also drilling in blocks in the Albertine basin dividing the two nations, which fought a 1998-2003 war that sucked in five other African countries.

Heritage and British-based Tullow Oil have discovered oil in the Albertine Basin, which spans the remote border. Tullow has three blocks, two in 50-50 partnership with Heritage. Between them they have drilled eight wells, all yielding crude.

The two companies say exploration is at an early stage but estimate reserves which could be in excess of a billion barrels.

They say they want to pump oil via a pipeline to the Kenyan coast, should they find more than 300 million barrels.

(Reporting by Tim Cocks; editing by Michael Roddy)

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