
The attack in Tatarszentgyorgy, a village 65 km (40 miles) southeast of Budapest, is the latest in a series on Roma houses in which seven people have died over the past year.
Peter Papp, criminal director of the county police, told MTI that a preliminary autopsy report showed the father and his son were shot dead. Two other children were hurt in the blaze.
Viktoria Mohacsi, a Roma Hungarian member of the European Parliament, told Reuters after visiting the scene that the two Roma were shot as they were trying to escape the house.
Local and national police declined comment, saying it was too early to give any details.
It was not immediately known whether the attack was racially motivated, but Mohacsi said Monday's attack resembled similar ones on Roma elsewhere in Hungary over the past year.
"I believe this (fire) could not have been caused by anything other than a petrol bomb," Mohacsi said.
"My assumption is that this attack was racially motivated," she added.
Erno Kallai, ombudsman in charge of national and ethnic minority rights, said in a statement that attacks on Roma people were alarming and he would raise this in parliament on Tuesday.
"In the past year there have been over 10, or according to some opinions even more, violent crimes committed against Roma families or their houses," Kallai said.
"A common feature of these cases is ... that perpetrators are still unknown," he added.
Hungary has one of the largest communities of Roma, also known as gypsies, in eastern Europe, making up 5 to 7 percent of the 10 million population.
A deepening recession and job losses is stoking resentment against the Roma in Hungary and has led to a strengthening of the far-right which fights against what it says is a rise in "Roma crime."
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