Although Hamas spokesman Usama Hamdan, who called the act "treason", did not name the country, most analysts believe he was referring to Israel's eastern neighbour, Jordan.
A car bomb killed Izz al-Din al-Shaikh Khalil, 42, and wounded three others on Sunday in al-Zahra district of Syria's capital.
Israeli television quoted unidentified security sources as saying Israel was responsible.
"This would be treason for an Arab security apparatus to be involved in this," Hamdan told al-Hayat daily on Monday.
He was responding to reports that an Arab country had given the Israeli spy agency Mossad information about the movements and habits of Hamas leaders abroad.
"Now, because of what happened yesterday or through other information, there are indications that this may be the case," Hamdan said.
The Hamas spokesman's comments were echoed on Monday by the newspaper of Syria's ruling Baath party.
Mahdi Dakhil Allah, al-Baath's editor-in-chief, said Khalil's slaying was "a result of the cooperation of Israel and some Arab security services".
He said he had "no evidence" to back up his accusations, but "it seems logical to think that".
Khalid Amayreh, Aljazeera.net's correspondent in the West Bank, said although no official source had named the suspected country all fingers were pointing at Jordan.
"The feeling here on the street is that Jordan is the number one suspect," he said.
"The secret services of Israel and Jordan have traditionally had a close working relationship, especially since the two countries signed a peace agreement in 1995.
"Many also believe that both countries see the Islamic movement in the region as their main enemy. The Islamic opposition in Jordan is seen by the ruling monarchy as the main obstacle to normalising relations with Israel."
"This would be treason for an Arab security apparatus to be involved in this"
However, Amayreh said a threat by Hamas' armed wing to target Israelis abroad after Khalil's assassination was just "an angry reaction".
"Hamas' policy has always been to confine attacks to Israel and the Occupied Territories and I don't think that is going to change," he said.
The Jordanian government has condemned Sunday's assassination, saying it aimed to destabilise security in the region and derail the Palestinian-Israeli peace process.
And Rim Allaf, a Middle East expert at London's Royal Institute of International Affairs, told Aljazeera.net there was probably no truth to the suspicions against Jordan.
"I don't think Israel needs Jordan to carry out an attack such as this," she said. "These may be unsubstantiated rumours or just media speculation.
The attack was Israel's second
foray into Syria in the past year
"The Israelis have said they had the addresses of all the Hamas leaders in Damascus. These leaders are very public figures and I don't think Israel would need any help finding them."
Moreover, Allaf said Syria was powerless to convincingly respond to Sunday's attack.
"Syria can't do anything about this - they are not in a position to do anything. They always say: 'We reserve the right to respond' and then they go to the UN and register a complaint.
"Basically, Syria is in a very difficult position. The rumours are that Hamas leader Khalid Mishaal has been told to leave Damascus and others have been told to keep a very low profile. But on the other hand, Syria's public position is that it supports the Palestinian cause."
Sunday's killing was Israel's second foray into Syria in the past year.
"I don't think Israel needs Jordan to carry out an attack such as this. These leaders are very public figures and I don't think Israel would need any help finding them"
Royal Institute of International Affairs
It was also the latest blow to the Hamas leadership which has claimed responsibility for many resistance attacks against Israel.
Israeli security officials vowed to renew an assassination campaign against Hamas leaders in Palestinian areas and abroad in response to twin bus bombings on 31 August that killed 16 people in the Israeli city of Beersheba.
Palestinian sources in Gaza said Khalil, who Israel deported to Lebanon in 1992, was believed to be in charge of the group's military wing outside the Palestinian territories.
However, Hamas sources in Beirut said he was only a mid-level official.