But in August Israeli authorities suddenly refused to renew his trading license because he was trading with "enemy" states Lebanon and Syria, frustrating both Abbasi's business and the Arab and Israeli readers he has helped interest in each other's literary traditions.
"How can the People of the Book be against books?" Abbasi asked, evoking the Jewish Bible as the first monotheistic holy text. "Books are a bridge to peace between cultures."
An Israeli Trade Ministry spokeswoman declined to explain the timing of the ban. But she cited a recent legal opinion that forbade importing goods from four countries Israel views as enemies – Iran, Iraq, Syria and Lebanon.
Israel has no diplomatic ties with Beirut or Damascus, so 57-year-old Abbasi uses Jordan and Egypt, the only Arab nations to sign peace deals with the Jewish state, as conduits.
Abbasi's original aim was to cater for Israel's 1.2 million minority Arab citizens, many of whom feel the perpetual absence of relations between Israel and its neighbors denies them cultural and ethnic ties to the Arab world.
But he branched out, and over the past 10 years has sold over half a million copies of some 16 Hebrew titles to Lebanon, Syria, Jordan, Egypt, Saudi Arabia, Qatar and other Arab countries, where the translated books reach Arab readers mainly through public libraries and universities.
From fact to fiction
Most are biographies of famous Israeli statesmen and military commanders, such as former prime ministers David Ben-Gurion and Golda Meir, or former armed forces chief Moshe Dayan, the general with the iconic eye patch.
But Abbasi has noticed a shift in Arab readers' tastes in Hebrew books. Last year, he sold over 30,000 copies of seven novels by Israeli writers in 15 Arab countries, including Syria and Lebanon.
"Arab readers ... are over the know-your-enemy mentality. Nowadays they want to know what Israeli novelists write about," Abbasi said.
Prominent Israeli actress Gila Almagor, whose semi-autobiographical novel Abbasi translated into Arabic and sold in Arab countries, said the decision to ban books from Syria and Lebanon was "arbitrary and stupid", especially as translation is funded by Israel's National Lottery.
"When I was told that my book would be translated into Arabic it was very emotional for me," said Almagor, whose book "The Summer of Aviya" depicts her childhood with a mother driven to insanity by their experiences during the Holocaust.
"My story is universal and I always believed that publishing it in Arabic would help give Israel and its people a face, an image other than that of the conflict," Almagor said.
From his office in an Arab neighborhood near the Port of Haifa, Abbasi said the ban would have a major impact on his business, given that Lebanon translates and prints more books in Arabic than any other country.
Lebanon's Publishers' Union said the country publishes 3,000 new titles every year, surpassing Egypt, Syria and Jordan.
"Children's books like Pinocchio and Harry Potter and thousands of works in many fields are translated and printed in Arabic only in Lebanon," Abbasi said.
'More than disappointing'
Among Abbasi's recent imports is "Gate of the Sun", a novel by Lebanese author Elias Khoury that explores the suffering of Palestinian refugees. The book, which Saleh translated into Hebrew, has been a hit with both Arabic and Hebrew readers.
"The ban is more than disappointing. It's a shock, especially for people like me who know that the best Arabic books come out of the capital of Arab culture, Beirut," said Ya'akoub Hijazi, an ardent reader of Arabic poetry and literature who is a 60-year-old Arab citizen of Israel.
Rana Idriss, manager of Lebanese publisher Dar al-Adab, said the ban was disastrous for business because Arab Israeli and Palestinian booksellers were a large chunk of her clientele.
"It's not a democratic step at all by a country that says it's open to thought," Idriss said. The ban amounted to "war" on Lebanese culture and Arab thought, she said.
In Syria, publishing firm Dar Cana'an translates and prints more than 15 Hebrew titles under government supervision, including some by renowned Israeli writer Amos Oz, Abbasi said.
Dar Cana'an's manager Saeed Barghouti said Israel's decision showed it had no interest in peace with Syria and Lebanon.
Abbasi said the ban could mean the end of his business.
"If the ban is final – and I plan to go all the way to the High Court – I have two choices: close or leave the country."