"Today they are here under the protection of our state, and personally of the president."
'Brought to tears'
Bakiyev had originally gone to Kazakhstan after leaving Kyrgyzstan, but he left on Monday, a day after Lukashenko had said Bakiyev would be welcome in his country.
"Bakiyev asked me to take him in several times. He wasn't asking for his own sake. That's what stunned me and brought me to tears. He said, 'Alexander, take my family. I fell sorry for my children, they're not guilty of anything'," Lukashenko said on Tuesday.
It was not clear which members of Bakiyev's family were in Minsk. One of his sons, Maxim, is wanted by the interim government amid accusations of corruption.
Edil Baisalov, a member of the interim government, told the Russian Interfax news agency on Tuesday that Bakiyev would only be allowed to return to Kyrgyzstan "in the capacity of a prisoner".
Meanwhile, Kyrgyzstan's interim rulersmoved to quell ethnic violence that has broken out since the ousting of Bakiyev.
Riot police and troops confronted a crowd of several hundred people on the outskirts of Bishkek on Tuesday, in an area where five people died on Mondayafter looters attacked homes belonging to mainly ethnic Russians and Meskhetian Turks.
Roza Otunbayeva, the leader of the interim government, has blamed the unrest on thugs trying to exploit the security vacuum to grab property illegally.
In the southern town of Jala'abad, Bakiyev supporters have been occupying government offices for several days, and have imposed their candidate as head of the regional police department.
Dmitry Medvedev, the Russian president, on Tuesday, called for Kyrgyzstan's interim government to hold elections to legitimise its authority if it wanted full-fledged economic co-operation with Russia.
"Essentially there is a need to resurrect the state and at present there is no state" in Kyrgyzstan, Medvedev said following talks with President Islam Karimov of Uzbekistan, a Central Asian nation that shares a border with Kyrgyzstan.
"And we expect Kyrgyzstan's interim government to undertake all the necessary and sufficient measures for that. The legitimisation of all the authorities, that is the holding of elections and not just de facto exercise of power is extremely important," Medvedev said.
"And only in this case can we develop full-fledged economic co-operation," he added in televised remarks.
Russia quickly recognised the Kyrgyz interim government, which has said it will run the country until elections can be held in six months, and offered to send humanitarian aid to the country.
At the same time, Medvedev indicated last week that the new authorities in Kyrgyzstan still had some way to go to win Moscow's full backing.
The new authorities on Monday pledged fast reform to strengthen the role of parliament at the expense of the president, and to hold free parliamentary and presidential elections in September or October.