The militant Islamic group figures on the EU's blacklist of terrorist organisations, making official contacts unacceptable, but the ministers suggested that such a government might lead to international recognition for Hamas.
"We have to evaluate how we get back onto the road map," said Finnish Foreign Minister Erkki Tuomioja, whose country, as current EU president, was hosting the informal talks in Lappeenranta, southern Finland.
"One of the priorities of course is we hope can get a government of national unity in the Palestinian territories which would be a credible partner for future negotiations whom nobody could refuse to talk to," he said.
For contacts with Hamas to begin, the EU and its partners in the international Middle East Quartet - the United Nations, Russia and the United States - demand that the group accepts three conditions.
Those include recognising Israel, calling an end to violence and accepting the validity of past agreements between the Jewish state and the Palestinians.
Hamas stunned the West when it swept to power early this year, but international embargoes on providing funds to its government have brought the Palestinian territories economically to their knees.
Despite its severe financial woes, it has resisted overtures by Palestinian leader Mahmud Abbas to enter into a government of national unity with his Fatah movement, which has dominated the Palestinian Authority in the past.
During their talks on the Middle East, the ministers, who examined several ways to strengthen the EU's influence in the region, underlined the important role that Syria could play.
Mr Tuomioja welcomed the decision by Damascus to respect an arms embargo against Hezbollah, the Shiite militia group in Lebanon that it backs, but he said the EU was waiting to see if that pledge would be put into effect.
Italian commandos land
Hundreds of Italian commandos will land in Lebanon today in the first major reinforcement to the United Nations mission monitoring a ceasefire between Israel and the Hezbollah Shiite militia.
The 878 elite soldiers from the San Marco and Lagunari regiments are embarking on what Italian Prime Minister Romano Prodi has called "a delicate mission, of enormous historical importance."
The troops are to begin landing on the beach in the southern coastal city of Tyre, said UNIFIL spokesman Alexander Ivanko.
Landing craft will ferry troops ashore at two locations in an operation
expected to last more than 16 hours, he said, adding that they would arrive with 132 wheeled vehicles, 10 armoured assault vehicles and 16 tracked vehicles.
Italy will assume command of UNIFIL in February.
Spain approves soldiers
Meanwhile the Spanish government has authorised the sending of 1,100 troops to southern Lebanon.
First Deputy Prime Minister Maria Teresa Fernandez de la Vega said the Spanish parliament would be asked to approve the sending of "up to 1,100 troops" next Wednesday.
The Turkish government has formally asked parliament to approve a motion authorising the deployment of peacekeeping troops in Lebanon.
A 900-strong French advance party is due to head on Monday to Lebanon.
German spy chief
Germany's spy chief has arrived in Beirut on a mission cloaked in secrecy, as the German foreign intelligence agency denied the visit was linked to efforts to negotiate a prisoner swap between Israel and Hezbollah.
Ernst Urlau, accompanied by a five-member delegation, flew into Beirut's international airport amid tight security and was met by German ambassador to Lebanon Marius Haas, the ANI news agency said.
A spokeswoman for the Federal Intelligence Service (BND) declined to discuss the purpose of Mr Urlau's visit, but denied reports he was serving as a go-between.
"The subject (of his talks) is not the prisoner exchange," she told AFP.
The German daily Sueddeutsche Zeitung reported yesterday, citing a BND officer, that Mr Urlau wanted to thank Beirut for its help in capturing suspects behind a failed attempt to bomb German passenger trains in July.
But a state secretary at the foreign ministry, Gernot Erler, said late Thursday that Mr Urlau was on his way to Lebanon following calls from Israel for help in securing the release of its two soldiers captured by Hezbollah in a deadly cross-border raid in July.
Israeli Foreign Minister Tzipi Livni has urged Germany to "work for the release of the kidnapped soldiers", while Lebanese Foreign Minister Fawzi Sallukh has also called on Germany to help resolve the hostage crisis.
Cluster bombs
The top UN humanitarian official in Lebanon says it will take more than a year to clear unexploded cluster bombs left over from the recent Israeli offensive in Lebanon.
But British-based demining Group, LandMine Action, said the clearing of unexploded cluster bombs in Lebanon could take 10 years.
"We will be clearing unexploded cluster munitions from the rubble of the villages of southern Lebanon for another decade," said Simon Conway, director of LandMine Action. "That is the grim reality," he told reporters in Geneva.
The UN humanitarian official, David Shearer, said about 100 foreign mine clearance and bomb disposal experts are expected to be working in Lebanon within a week.
Up to 100,000 unexploded cluster bombs are thought to remain in south Lebanon, according to the UN humanitarian coordination office.
Mr Shearer estimated that about 40 percent of the bomblets contained in cluster bombs had not exploded and called on Israel to provide information on the locations where cluster bombs were used.
Russian FM visit
Russian Foreign Minister Sergey Lavrov will visit the Middle East next week, with stops in Lebanon, Syria, Israel and the Palestinian territories.
Mr Lavrov's visits on Thursday and Friday will focus on "the situation in Lebanon in the context of starting to implement UN Security Council Resolution 1701," the Russian foreign ministry told the Itar-Tass news agency.