The latest suspect, a Bulgarian national, was taken into custody late Saturday evening in Budapest, according to a police statement.
Three Bulgarian citizens and an Afghan citizen had already been arrested in connection with the truck full of people, who were likely fleeing war-ravaged Syria
. Austrian authorities suspect a Bulgarian-Hungarian smuggling ring.
Sixty of the 71 victims were men. Eight women died, as did three children, ages 2, 3 and 8.
Hungary is under increasing pressure from Western European countries to change its approach to the migrant crisis.
France's Foreign Minister Laurent Fabius said Sunday he is shocked by the escalating migration crisis and accused eastern European countries like Hungary of not respecting European values.
"Each country needs to find a solution. France and Germany are part of these countries. When I see some European countries that don't accept quotas of migrants I find it scandalous. Especially East European countries," he said on a popular Sunday morning program on Europe 1
Hungary has been erecting a barbed wire fence along its more than 100-mile border with Serbia, which Fabius said should be taken down.
"Hungary is very severe. Hungary is part of Europe. Europe has some values and it doesn't respect these values. Like this razor wire barrier they built."
The European Union has been trying to find ways to ease the migrant pressure on Italy and Greece, where most migrants enter Europe, but many EU member countries, including Hungary, have been reluctant to accept a voluntary quota.
The foreign ministers of Germany, France and Britain issued a statement Friday asking a special EU council to meet in the next two weeks to work on measures to better organize the influx of migrants.
They're asking for the implementation of "hot spots" in Greece and Italy by the end of this year. These hot spots would register the number of migrants and identify those who need protection, according to the statement.
More migrants die crossing Mediterranean
A boat carrying migrants sank off the coast of Libya on Saturday, killing at least seven, according to the Red Crescent in Tripoli.
The coast guard is recovering the bodies, according to spokesman Mohamad al-Misrati.
"We are now receiving unconfirmed reports that there are more dead people who were on that boat," said al-Misrati. "It could be that up to 30 people died but we are still checking."
Officials said that they believe the boat that sank was on its way to the Italian coast.
Pope prays for migrants
Pope Francis appealed for prayers for migrants during an address in St. Peter's Square on Sunday.
He called on people to work together to prevent tragedies like the death of the 71 migrants in the truck on the Vienna-Budapest highway, which he said "offends the entire human family."
"For all these brothers and sisters, I pray and ask you to pray," he said.