Mr Poznyak, leader of the Belarussian Popular Front, a nationalist opposition movement, left Belarus in April while under threat of arrest for organising rallies against Mr Lukashenko's policy of forging an economic and political union with Russia. If he and Mr Naumchik, his assistant, were to be granted asylum, it would be the first such case involving any former Soviet republic since the Soviet Union's collapse in 1991.
Opposition politicians say this would seriously tarnish Belarus's international image, already battered by Mr Lukashenko's reputation for idiosyncratic, pro-Russian authoritarianism. "There is constant pressure on the opposition. We cannot conceal the fact that human rights are repeatedly violated. Even parliament has no access to state television," said Pyotr Kravchenko, a former foreign minister.
The US State Department, which advises immigration officials on granting asylum, may take the view that Mr Poznyak and Mr Naumchik would not be in danger of severe persecution if they returned to Belarus. But US diplomats are under few illusions about Mr Lukashenko's rule. "We've been concerned by a lot of the actions of the government and been concerned by some infringements of human rights," said Nicholas Burns, the State Department spokesman.
Since coming to power in 1994 Mr Lukashenko has suspended trade unions, dismissed newspaper editors and ordered a crackdown on "anti-presidential actions". About 200 people received short jail terms for taking part in opposition-led demonstrations in spring, and on Monday, Mr Lukashenko banned rallies for the duration of Belarus's harvest.
His repressive policies and enthusiasm for union with Russia have prompted a backlash, with seven opposition parties, from nationalists to Communists, signing a declaration last week that denounced Mr Lukashenko and warned of the danger of totalitarian rule.
Undeterred, the President is seeking constitutional changes that would extend his term in office from five to seven years, enabling him to rule unchallenged until 2001.
If Mr Lukashenko cares about his image in the US, he did himself no favours last Thursday by appearing to lend credence to a wild accusation from a Communist member of the Russian parliament that the CIA is plotting to overthrow him.
Viktor Ilyukhin alleged that the CIA had set up a base in Warsaw to engineer Mr Lukashenko's fall by means of strikes and street protests.
US diplomats dismissed the allegations as nonsense. It did little to improve the atmosphere of US-Belarussian relations, which suffered last year when Belarussian border guards shot down a hot-air balloon taking part in a European race, killing the two US pilots.Reuse content