Syria has been accused of involvement in al-Hariri's assassination in order to maintain control over Lebanon. Syria has denied any role.
"It is very important to understand that Syria has a big potential role to play in stability in the Middle East," Miliband told BBC radio on Tuesday.
"Over the last 18 months, I have been talking with the Syrian foreign minister about ... Syria's responsibilities in the region in respect of counter-terrorism, in respect of Iraq, in respect of the Middle East peace process," Miliband said.
"It can be a force for stability or it can be a force for instability."
The US has accused Syria of turning a blind eye to groups fighting against the US military in Iraq, but diplomatic contacts between Europe - notably France and Britain - and Damascus have increased in recent months.
The British foreign secretary also met other senior Syrian leaders on Tuesday, including his counterpart, Walid Moualem, who said the talks laid down the foundation for strong ties between the two countries.
|Miliband has welcomed Syria's 'new approach' to regional diplomacy [AFP]
In London last week, Miliband welcomed Syria's "new approach" to regional diplomacy, saying it could help stabilise the Middle East.
Britain has supported ongoing rounds of indirect peace talks between Syria and Israel, which have been brokered by Turkey.
Those negotiations have revolved around the Golan Heights, a strategic plateau that Israel captured from Syria during a Middle East war in 1967.
Damascus has also come under increasing pressure from the US to police its western border with Iraq.
Washington says the 2,000km-long border is a route for smugglers and foreign fighters who go on to launch attacks in Iraq.
Miliband's visit comes as the United Nations' nuclear inspectorate prepares to report its findings on samples gathered from the site of an alleged nuclear reactor in Syria, which Israeli aircraft bombed in September 2007.
Mohammed ElBaradei, head of the International Atomic Energy Agency, said on Monday that traces of uranium found at the site in June are not sufficient evidence of a covert nuclear programme.
Uranium particles discovered thus far by IAEA investigators in Syria were not enriched to a level suggestive of a nuclear weapons programme, he said.
"[The uranium] could have come in so many different ways ... We are looking at so many different scenarios," he said.
"We need co-operation from Syria; we need co-operation from Israel. I would still like more transparency from the Syrians."