WASHINGTON – A bounty of $5 million each now rests on the heads of two Sudanese terrorists who took part in the murder of a Buffalo-born diplomat five years ago.

And Rep. Brian Higgins said that such a big-money reward, offered by the State Department Tuesday, may be just what’s needed to find the fugitives who took part in the killing of John M. Granville, a Canisius High School graduate who was working for the U.S. Agency for International Development.

Higgins, D-Buffalo, indicated that the State Department may be offering the rewards now because the search for the two men has moved way beyond the wild-goose-chase phase.

“Perhaps they look to targets that are realistic when offering this kind of money,” said Higgins, who discussed the case with a top USAID official on Tuesday. “I think they’re closing in on them.”

The men being hunted – Abdelbasit Alhaj Alhassan Haj Hamad and Mohamed Makawi Ibrahim – were among four who ambushed and killed Granville and his driver in the Sudanese capital, Khartoum, on Jan. 1, 2008. Sudanese police identified the four murderers as Islamic extremists who attacked Granville and Sudanese USAID employee Adbelrahman Abbas Rahama out of a hatred of America.

Hamad and Ibrahim and two co-conspirators were convicted of murder and sentenced to death in a Sudanese court in 2009. But a year later, they escaped from prison through a sewage pipe in what the Sudan Tribune called a “Shawshank Redemption-style prison breakout.”

One of the escapees, Abdul Rauf Abuzaid, was recaptured in June 2010, and another was killed in Somalia in 2011, the State Department said.

But Hamad and Ibrahim remain at large, much to the distress of Granville’s family.

“I find it incredibly hard to believe that these four men just got out through a sewer pipe and had a car waiting for them,” Paul F. Granville, a cousin of the slain diplomat’s late father, said after the murderers escaped.

Higgins, who lives four blocks from where Granville grew up in South Buffalo, has been working on the matter with the Granville family for years, and he pressed the State Department to offer the reward.

“We think this is a major breakthrough,” said Higgins, who serves on the House Foreign Affairs Committee. “Money is important in that part of the world, as it is everywhere – especially a reward of this magnitude. I think it will be helpful in apprehending the murderers.”

Higgins discussed the case Tuesday with Earl W. Gast, assistant administrator for Africa at USAID. Afterward, Higgins said the fugitives could now be allied with al-Shabaab, the dominant terrorist group in Somalia.

“My sense is that they [federal authorities] have more information than they’re sharing, obviously, about their whereabouts,” Higgins said.

The money is being offered under the State Department’s Rewards for Justice program, which Congress created in 1984 to help find those who have planned – or are planning – terrorist attacks.

Since its inception, the program has paid out more than $125 million to more than 80 people who provided information that led to the arrest of terrorists or the prevention of terrorist attacks, the State Department said.

In addition to announcing the reward on Twitter, the State Department said in a statement that it is freezing the assets of Hamad and Ibrahim and forbidding Americans from participating in any financial transactions with them. “This action will help stem the flow of financial and other assistance to these terrorists,” the State Department said in a statement.

Granville, 33, was a former Peace Corps volunteer who was in Sudan working to implement a peace treaty in that war-torn country.

The offer of the reward came as good news to William J. Hochul Jr., the U.S. attorney for Western New York, who traveled to Sudan to work on the case during his days as an assistant U.S. attorney and who has been pressing the matter ever since.

“This reward is the latest step in our five-year fight to bring the killers of John Granville and Abbas, his driver, to justice,” Hochul said. “John’s family, his Western New York community, and our entire country deserve no less.”