The ultra-conservative Islamist insurgents spent more than two days at a plush hotel in central Moscow, where they met several leading Afghan politicians -- including past president Hamid Karzai and former warlord Atta Muhammad Nur.

In a joint statement, the parties said they'd had "productive and constructive" discussions focusing on issues including a possible ceasefire, the "strengthening of the Islamic system" and "women's rights".

"Both sides have had tremendous progress, but some issues require further discussions," the statement read.

But with the Kabul administration -- viewed by the Taliban as a US-backed puppet regime -- once more sidelined from the conversation, it was difficult to see what tangible results could come from the talks.

Afghan President Ashraf Ghani had proposed a nationwide ceasefire at the start of the holy month of Ramadan, but the Taliban rejected the offer.

The Taliban have also baulked at repeated US calls to reduce violence while negotiations between the insurgents and Washington are ongoing.

The meeting in Moscow was the second such summit in the Russian capital.

The bearded, turban-wearing Taliban were photographed looking uncomfortable as female reporters in figure-hugging Western clothing approached them for interviews.

The meeting came weeks after a sixth round of talks between the US and Taliban wrapped up in Qatar with no tangible progress cited by the negotiating teams.

Those talks, led by US peace envoy Zalmay Khalilzad, appear to have stalled over the fundamental question of when foreign forces would depart Afghanistan in the event of a peace deal.

The US has refused to agree to a withdrawal until the Taliban put in place security guarantees, a ceasefire, and other commitments including an "intra-Afghan" dialogue with the Kabul government and other Afghan representatives.

But the Taliban insist foreign forces leave first.

- Women's 'rights' -

While parties claimed the Moscow summit was an "intra-Afghan" meeting, representatives from Ghani's government -- as well as anyone from the US -- were conspicuous in their absence.

At the start of the summit, initially convened by Moscow to mark 100 years of Russian-Afghan ties, the Afghan ambassador to Russia was allowed to give a speech.

But he was barred from subsequent events, so ended up sitting in the lobby of the swish hotel.

Still, Sher Mohammad Abbas Stanikzai -- the Taliban's chief negotiator and former deputy minister of foreign affairs -- insisted the insurgents were seeking peace "with all sincerity".

"But we want a reasonable peace in Afghanistan... the occupation has to end," he said.

Taliban spokesman Suhail Shaheen said the group envisions a future government in which "all Afghans would see themselves".

Since peace talks began last autumn between the Taliban and the US, the insurgents have insisted they have moderated some of their views -- including the rights of women, who were brutally repressed under their 1996-2001 totalitarian regime.

The Taliban want an "Afghanistan where the rights of women, men and children, old and young are ensured," Stanikzai said.

However, those rights would be framed through Sharia law and tribal tradition, and so open to broad interpretation by men.

Meanwhile, violence continued apace in Kabul and across Afghanistan.

On Thursday, a suicide bomber attacked a military academy in the capital, killing six.

And Afghan intelligence officials said 62 Taliban fighters were killed Wednesday night in the central province of Wardak.