(CNN) -- A bus bombing that killed five Israeli tourists, the bus driver and the suspected bomber in Bulgaria was probably carried out by a male suicide attacker who had a fake Michigan driver's license, Bulgaria's interior minister said Thursday.
Israel said it suspects Iran or an Islamist militant group was behind the attack, which occurred Wednesday in a parking lot outside Burgas International Airport in Bulgaria. Tensions between Israel and Tehran have been escalating in recent months.
In a televised statement Thursday, Israeli Prime Minister Benjamin Netanyahu said the attack was "perpetrated by Hezbollah, Iran's leading terrorist proxy," as part of a global campaign that has reached a dozen countries on five continents.
But he offered no evidence. Israel's U.S. Embassy said Wednesday that it had no proof that Iran was the instigator of the attack.
Netanyahu said Hezbollah and Iran have been trying to foment terrorism in countries that include Kenya, India and Cyprus, as well as in the United States, where an Iranian tried to kill the Saudi diplomat.
He urged world powers to expose Iran as "the premier terrorist-supporting state that it is" and prevent it from developing "the world's most dangerous weapons," a reference to its nuclear program.
"We will continue to fight against the terrorists and exact a heavy price from those that support them," Netanyahu said.
Iran's Foreign Ministry spokesman, Ramin Mehmanparast, said Israel was engaging in "baseless accusations against other countries in order to distract the attention of the international community from its terrorist activities being carried out throughout the world," according to a statement from the state-run IRNA news agency.
"The Zionist regime as master of state and organized terrorism has its hands in (the) blood of innocent Lebanese, Palestinian and other nationalities," Mehmanparast said.
The Iranian Embassy in the Bulgarian capital, Sofia, said earlier that Israeli suggestions that Tehran was involved in Wednesday's attack were "unsubstantiated" and that the assertion was politically motivated.
The identity of the man thought to have put a backpack bomb on the bus remained a mystery, but he was carrying a Michigan driver's license that FBI officials say was fake, Bulgarian Interior Minister Tsvetan Tsvetanov said.
Fingerprints were being checked, and investigators were at the scene to collect evidence, he said.
Meanwhile, a third and final Israel Air Force aircraft left Bulgaria Thursday for Israel, this one carrying coffins holding the bodies of the victims, the Israel Defense Forces said in a statement.
The aircraft was to land at Ben Gurion Airport in Tel Aviv, where the coffins were to be received in an official ceremony.
Thirty-three Israelis wounded in the blast arrived earlier Thursday in Tel Aviv.
Maj. Gen. Itzik Kreis of the Israel Defense Forces said at the airport that one of the wounded was in critical condition.
Israeli Defense Minister Ehud Barak warned of consequences for those responsible.
"We will find those who executed this attack and those who sent them," he said.
At the United Nations, the Security Council issued a statement condemning the attack.
In all, 32 people were hospitalized, some of them in critical condition, said Bulgaria's permanent representative to the world body, Stefan Tafrov. Two Russians, an Italian and a Slovak national were among the victims of what he called "the largest terrorist attack against Bulgaria in our modern history."
Asked if Iran or Hezbollah was responsible, he said, "As of today, we don't know. We simply haven't identified the responsible country or organization or entity. We can't exclude anything, but we haven't identified the force, the organization behind this attack."
"I can't get into the details of the investigation, which, of course, is still going on," Israel's deputy permanent representative to the United Nations, Haim Waxman, told reporters. "We know the fingerprints are very clear: The hands of Iran and Hezbollah are all over this attack."
Regarded by the United States and Israel as a terrorist organization, Hezbollah is a Shiite militant group that holds power in the Lebanese government. It is financed and armed by allies Iran and Syria.
Bulgaria, whose Black Sea beach resorts are a popular destination for Israelis, has not speculated on who may have been responsible for the attack. Bulgaria received nearly 8.4 million visitors in 2010, the last year for which U.N. World Tourism Organization figures are available. The vast majority of the country's visitors that year, more than 8 million, came from Europe. About 25,000 visitors came from the Middle East.
Tsvetanov sought to reassure those alarmed by the attack.
"I can assure you that we're doing all we can to strengthen security in all the areas where it might be necessary to do so," he told Bulgarian station TV7.
The Iranian Embassy statement said Iran condemns all terrorism.
"Iran and Bulgaria are friends, and they follow their relationship on the basis of mutual respect and interests," it said. "The rotten tricks of the enemies can never shake the stability of this friendship."
Iran's state-run Press TV also quoted Iranian spokesman Mehmanparast as telling the Arabic-language Al-Alam television network that Iran condemns the attack.
"The Islamic Republic of Iran, which itself is the biggest victim of terrorism, considers any act that endangers the lives of innocent people in order to fulfill illegitimate political objectives as inhumane and strongly condemns it," Mehmanparast said.
Bulgarian authorities believe that the bomber was carrying the bomb in a backpack, which he placed in the luggage compartment underneath the carriage, Tsvetanov said. The bus was to have taken about 47 passengers to a resort.
Security footage aired by Bulgarian National TV shows the man believed to be the bomber, who is white with long hair and wearing khaki shorts, a baseball cap and sneakers. He appears relaxed as he walks among other travelers, carrying a backpack and a smaller bag.
Tsvetanov had earlier said another person died overnight from the blast, but he subsequently said the Israeli ambassador had misinformed him.
According to a U.S. State Department International Religious Freedom Report, released in September, more than 80% of Bulgaria's 7.6 million residents are Orthodox Christian, with Muslims making up the largest minority at about 13%. Jews make up fewer than 5% of the country's population, the report says.
U.S. President Barack Obama condemned the "barbaric terrorist attack."
"As Israel has tragically once more been a target of terrorism, the United States reaffirms our unshakeable commitment to Israel's security, and our deep friendship and solidarity with the Israeli people," said Obama, who called Netanyahu to express his condolences.
CNN's Guy Azriel, Paul Colsey, Raja Razek, Boriana Milanova, Stephanie Halasz, Ralitsa Vassileva, Laura Smith-Spark and Jennifer Deaton contributed to this report.