The behaviour of some Muslim members of Sweden's Green Party - part of a coalition government - has sparked a debate in the country on whether the environmental group is becoming influenced by religious conservatives.

The party has been put in the media spotlight after a series of controversies, including one members' refusal to shake hands with women and another doing hand signs associated with Egypt's Muslim Brotherhood in the background of a live TV broadcast.

Housing Minister Mehmet Kaplan, a Green Party member and former leader of a Swedish Muslim youth group, resigned last week after a newspaper published pictures of him attending a dinner where members of the Turkish far-right group the Grey Wolves were present.

He denied any wrongdoing and the party leadership defended him until the end, but he stepped down when a video surfaced of Kaplan comparing Israel's treatment of Palestinians to how the Nazis persecuted Jews.

"Israelis today treat Palestinians in a very similar way to how Jews were treated in Germany in the 1930s," he told a seminar in 2009.

After his resignation, new images emerged in which Kaplan and other Muslim members of the Green Party were seen holding up four fingers, a hand gesture used by the Muslim Brotherhood in Egypt.

The so-called Rabaa sign emerged after a massacre in Cairo's Rabaa al-Adawiya square where hundreds of people were killed as Egyptian security forces broke up a sit-in launched by members of the Brotherhood.

Lars Nicander, director of the Centre for Asymmetric Threat Studies at the Swedish National Defence College, told Swedish TV4 last week he saw similarities with how the former Soviet Union tried to infiltrate parties during the Cold War, "as people close to the Muslim Brotherhood, an Islamist party, obviously have gained a strong foothold in the Green Party".

"I see a similarity to how Soviet communism was acting during the Cold War when it tried to infiltrate the various democratic parties," said Nicander.

Green Party leaders said on Monday there was no evidence of Islamists influencing party policies.

Many Green Party members have questioned whether the Brotherhood's conservative views are compatible with the feminist and gay-friendly platform of the Swedish Greens.

Too 'intimate'

The biggest outcry came after Yasri Khan, a 30-year-old running for a seat on the Green Party's executive board, refused to shake the hand of a Swedish TV reporter.

He said shaking hands with someone from the opposite sex is too "intimate", and instead put his hand on his heart in a Muslim greeting.

A debate ensued in Sweden, with Khan's critics calling his behaviour insulting to women and his supporters dismissing the criticism as Islamophobia.

Prime Minister Stefan Lofven weighed in, saying that in Sweden "you shake hands with both women and men".

Khan withdrew his candidacy for the Green Party executive board and also quit his seats on a regional board and city council.

He told the AP news agency he was keeping his party membership for now, though he questioned whether practising Muslims are still welcome in the party.

"I think the Green Party needs to work on their inclusive values," he said. "How do you combine diversity and religion with an ethnocentric and prejudiced idea of gender equality?"

Asked whether he would describe himself as an Islamist, he said he did not even know what the word meant.

"If it means a practising Muslim who is contributing to politics, then I'm an Islamist - or was, since I'm leaving. But if it means a terrorist or against gender equality then I am as far away from an Islamist as you can get," Khan said.