‘We are moving towards a general understanding that encompasses the expectations and visions of the parties,’ Ismail Ould Cheikh Ahmed said in a statement.
‘The discussions have become more sensitive and delicate bringing us closer to a comprehensive agreement,’ he said.
Ould Cheikh Ahmed is to brief the UN Security Council in a closed session later on Wednesday on the progress made in the peace talks which began on April 21 but have been clouded by repeated walkouts by the government delegation.
Face-to-face meetings resumed on Monday for the first time in nearly a week after the latest government boycott.
Ould Cheikh Ahmed said discussions on Tuesday centred on ‘various military and security issues including withdrawals and troop movements’.
‘We are now working on overcoming various obstacles and addressing specific details of an implementation mechanism,’ he said.
The apparent progress comes after Foreign Minister Abdulmalek al-Mikhlafi said on Monday that the government stood ready to make concessions for the sake of peace.
The government had insisted that rebels should implement an April 2015 Security Council resolution demanding their withdrawal from the capital and other territory they have seized since 2014.
Despite a 14-month-old Saudi-led military intervention in support of President Abedrabbo Mansour Hadi's government, the Houthi Shia rebels and their allies still control many of Yemen's most populous regions, including the central and northern highlands and the Red Sea coast.