By Adrian Croft

LONDON, Feb 20 (Reuters) - An exiled former anti-corruption adviser urged Kenyans on Wednesday to tackle graft and push through land and constitutional reforms as part of a package to end a political standoff after disputed elections.

Former United Nations chief Kofi Annan is mediating in talks between President Mwai Kibaki and the opposition aimed at ending a political crisis that sparked an explosion of ethnic violence in which more than 1,000 people have been killed.

John Githongo, who quit as Kenya's first anti-corruption adviser in 2005 and later blew the whistle on one of Kenya's biggest graft scandals, said constitutional reform was needed now to crimp the powers of the Kenyan president.

"Anybody who wins the presidency under today's constitution of Kenya, will face the same problem we had before," he said at a debate hosted by the Royal Commonwealth Society in London.

"You're a demi-god (as president). It allows impunity. You can appoint anyone, everyone, you can sack people at will, appoint your relatives ... Introducing accountability to the executive is something that is extremely important."

Githongo, who now lives in Britain, called for greater parliamentary oversight over the president's powers to appoint judges and other key officials.

Kenya's Electoral Commission had no credibility and needed a "complete overhaul", he said. "I'm quite shocked and surprised that it hasn't already resigned ... It's outrageous."

"These people should all be removed immediately, but then appointed in a manner that is more transparent."

Opposition leader Raila Odinga says the Electoral Commission, which declared Kibaki the winner three days after the Dec. 27 presidential election, is biased.

Githongo urged Kenyans to address long-standing issues over land reform and corruption and said a small, identifiable minority benefited from graft, creating tremendous resentment.

The reforms he was calling for would not wait for a government of national unity but could be tackled now, he said.

"I think it's all part of one big package," he said.

The opposition accuses Kibaki's team of stealing the election. Kibaki says he won fairly and accuses Odinga's Orange Democratic Movement (ODM) of instigating tribal violence that displaced 300,000 people in East Africa's biggest economy. (Editing by Michael Winfrey)

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