Belarus says Warsaw's support of Milinkevich amounts to interference.
Relations between Poland and Belarus have been strained for some time.
Last year, Minsk and Warsaw became involved in a series of tit-for-tat diplomatic expulsions that started after Lukashenka accused Poland of interference.
The United States and some European powers have described Lukashenka's government as the last dictatorship in Europe.
Syarhey Haydukevich, who was born in 1954 in Minsk, served in the Soviet Armed Forces in 1976-91, rising to the rank of colonel. From 1982 to 1984, he was a Soviet military adviser in Iraq. In 1992-94, Haydukevich was chairman of the government's committee for the social protection of employees of state security bodies, the Interior Ministry, the Defense Ministry, the Border Troops, and soldiers who participated in Soviet military operations abroad.
As the head of the Belarusian Liberal Democratic Party, he has been criticized by party members for his allegedly authoritarian practices and for the party's poor performances during recent parliamentary and presidential elections. In the 2001 presidential election, Haydukevich won 2.5 percent of the vote.
In June 2005, a Minsk court ordered opposition daily "Narodnaya volya," to pay 100 million rubles ($46,500) in damages to Haydukevich for defaming him in an article published in March. The article suggested that Haydukevich was involved in the illegal sale of Iraqi oil under quotas received from the regime of Saddam Hussein.