HARARE (Reuters) - Zimbabwe's tobacco auction opened on Tuesday but trading was postponed a week with farmers demanding a weaker exchange rate to shore up earnings from a crop that was once the country's top foreign currency earner.

If farmers continue to withhold their crop, it could spell more trouble for President Robert Mugabe's government which is battling acute shortages of foreign exchange, food, fuel and the world's highest inflation rate of nearly 165,000 percent.

Tobacco exports used to be the major source of foreign exchange, but have been replaced by gold as sales of the crop steadily dropped from 236 million kgs in 2000, a trend blamed partly on Mugabe's controversial land reforms.

At the main tobacco auction in Harare, floors opened on time but had to close after dozens of small-scale farmers refused to sell, demanding a revision of the exchange rate.

"The tobacco auctions opened today but there was no trade because there are concerns which are still being discussed and so we have postponed the auctions by a week until they have been resolved," said Andrew Matibiri, the general manager of industry regulator Tobacco Industry and Marketing Board.

Farmers said the official exchange rate of 30,000 Zimbabwe dollars to the U.S. dollar was way below the black market price of $1 to 90 million Zimbabwe dollars which producers of inputs use to calculate prices.

Tobacco farmers are paid 80 percent of their earnings in local currency and the remainder in U.S. dollars.

"We want the government to review the exchange rate otherwise we will have to leave tobacco production which has become very expensive," a farmer told Reuters outside the main auction floor in Harare.

Tobacco output fell to 68.8 million kgs last year, generating around $160 million, a significant amount for a country whose foreign earnings continue to dwindle in line with a collapsing economy.