European governments including Britain have stepped up back-channel contacts with Hamas despite an official EU policy of political isolation, in an effort to understand and possibly influence debate in the Islamist group about its future direction, according to four senior Hamas officials.

Meetings between Hamas and European government representatives and intermediaries have taken place in Gaza, Cairo and European capitals over recent months, the officials said.

The EU banned contact between its member states and the Islamist organisation when the latter took over Gaza in 2007, and Hamas is classified as a terrorist organisation by Brussels.

The Hamas officials, who spoke to the Guardian over recent weeks, declined to give specific details of meetings. "These countries trust us not to disclose information about contacts," said Ahmed Yousef, a member of Hamas's decision-making body, the shura council, and a former deputy foreign minister.

"We try to keep the contacts low-profile because it causes trouble. We prefer not to talk about it but I can guarantee that most European countries are interested in opening doors to Hamas."

Britain was among the EU countries mentioned by the four Gaza officials as having recent contact with Hamas. Others included Sweden, Denmark, the Netherlands, France, Italy and Spain.

The UK, Netherlands and Sweden denied official government-level contact; spokesmen for the other countries did not respond to requests for comment. Norway and Switzerland, neither of which are EU members, are open about their links with Hamas representatives.

"Some activities are not at official levels, but there are also some at official level, away from the media," said Basem Naim, who is in charge of foreign affairs in the Hamas government in Gaza and a former health minister. "We have met some ambassadors and some government officials."

Ghazi Hamad, the deputy foreign minister, said he had met European government representatives, including ambassadors and consuls, in recent weeks. Most of his interlocutors "believe the policy of isolation must end and dialogue must open", he said.

Taher al-Nounou, a spokesman for the Hamas government, said he had met officials and former officials in Europe, and further meetings were planned. "All countries refuse to declare these meetings because they tied their hands by putting Hamas on the EU terror list," he said.

Hamas stressed that the purpose of the meetings was not negotiations but to establish links and open dialogue.

"Hamas is a fact on the ground, an active part of Palestinian politics," said Naim. "This is well known to all players, inside and outside [Palestine], including those in Europe. Anyone who wants to influence the politics on the ground has to take this into consideration."

Al-Nounou cited three main purposes to approaches from EU states. "Firstly, they want to know about our vision for the peace process, and whether Hamas's position is changing. They want to know if Hamas is for political or military methods, and compare the positions of Hamas now and in the past," he said.

"Secondly, they believe Hamas is an important player in Palestine and in the region, and that they need to deal with us. Thirdly, they try to put pressure on us to accept the quartet demands."

The Middle East quartet – the US, EU, UN and Russia – has set three principles that Hamas must accept for its isolation to end: renouncing violence, recognising Israel and abiding by previous diplomatic agreements.

But Hamas believes that many European governments now see the isolationist policy of the EU and US as a mistake, particularly in the aftermath of regional uprisings over the past two and a half years.

Western countries have opened political dialogue with Islamist organisations which have taken power, yet continue to ban contact with Hamas.

However, the four Hamas officials spoke to the Guardian before the recent military takeover in Egypt. The removal of Mohamed Morsi as president and the crackdown on the Muslim Brotherhood may check any contacts.

Meanwhile, the supposition that isolation would weaken Hamas has not been borne out. Although Hamas by no means enjoys universal support in Gaza, it has become more entrenched over the past six years.

"After six years of total isolation, boycott, the policy has failed," said Naim. "You cannot close your eyes and put your head in the sand and say Hamas is not here. I have met with many Europeans at different levels and they all say the policy was a big mistake."

According to Omar Shaban, the politically independent director of PalThink, a Gaza-based thinktank, European countries realise that "Hamas has to be part of the dialogue around the political future". Not only do they need to understand Hamas, he said, but they are also asking if Hamas can be influenced. "They've realised they should not sit in Brussels and wait for Hamas to change. The international community needs to be proactive."Some European countries would like to see Hamas taken off the EU terror list, said the Hamas officials. "They see Hamas has a new face – more realistic, more pragmatic, more co-operative," said Hamad, one of the organisation's more moderate figures. "It's very clear to them that Hamas must be lifted from the terror list and dealt with as a partner and a main player in the region."

Britain was one of the countries eager to meet Hamas, said Nounou, but was constrained by EU policy. "They have tried to open some channels with us, not directly, but through unofficial organisations."

Naim said Hamas officials had met interlocutors who intended to report back to the UK government. This was not clearly stated, he added, "but we have an understanding".

A British government source denied "doing anything covert" but said it had got "messages and information to and from Hamas" through channels. The source added: "We know some governments are in contact. Clearly at some stage, the likelihood of involving Hamas [in the political process] is high." The question of whether the EU policy was tenable "comes up quite regularly for us to consider".

A European diplomat said he would be surprised if any EU member states were engaged in direct contacts. "The risks are too high. It's just about possible it's happening, but unlikely."

The Hamas officials said they also have contact with the US but through third parties. All four spoke of meetings with former US officials and advisers, described by Naim as "back-channel talks with people close to the White House".

According to Yousef, "the Obama administration is turning a blind eye" to unofficial contact, "not like it was before".

Shaban said he expected contact with the international community to increase over the coming months and years. "The Europeans and Americans are pragmatic."

Israel, however, was committed to a "psychological blockade", he said. "It's easier to say 'no compromise' than to compromise. Israel prefers the easy path."

Israel dismissed Hamas's claims to be in regular contact with European countries. "The denials by Hamas's supposed partners says a lot," said Yigal Palmor of the foreign ministry. "But by claiming this, Hamas looks palatable, diplomatic, prestigious and successful. It sends a good message to its own constituency: that it is not as isolated as people say."

Until Hamas met the quartet's conditions, it could not be considered an interlocutor, he added. "Hamas is not willing to even consider meeting these criteria."