"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.
He clarified on Twitter that he will make the briefing by video conference from Kuwait.
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.
A Western diplomat familiar with the talks said they had made important progress.
"We are in a stage where the parties have to make hard choices and compromises," the diplomat told AFP, adding that he was "very optimistic" that a deal could be reached.
"We have not seen this momentum towards peace in the past one and a half years... a roadmap plan has been laid down... and it has to work," he said.
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- 'National Salvation Government' -
The main sticking point in the talks has been the form of government to oversee a transition.
Huthi Shiite rebels and their allies have demanded a unity government.
The government delegation insists that the legitimacy of President Abedrabbo Mansour Hadi must be respected.
The government has also demanded that rebels implement an April 2015 Security Council resolution demanding their withdrawal from the capital and other territory they have seized since 2014.
To overcome this problem, the UN envoy has proposed a "National Salvation Government," the Western diplomat said.
The proposed government "would be formed on a consensual and inclusive basis and in accordance with the legal references, and would only replace the current government once Sanaa and key government institutions are not under the control of non-state actors," he said.
Huthi spokesman Mohammed Abdulsalam warned that if no fair solution was reached, the rebels would form the government in Sanaa.
"Yemenis are awaiting a fair solution and if it fails, anti-aggression national forces must fill the vacuum by forming a government to serve the people and confront challenges," Abdulsalam said on Twitter.
The rebel delegation met late Tuesday with the ambassadors to Yemen of the United States, Britain and the European Union and called for the formation of a "consensus executive authority" in Yemen.
They also accused Saudi Arabia of violating the ceasefire, sources close to the delegation said.
Reporters Without Borders urged the rebels to release 10 journalists who began a hunger strike on May 9 to protest against their detention.
Despite a 14-month-old Saudi-led military intervention in support of Hadi's government, the rebels and their allies still control many of Yemen's most populous regions, including the central and northern highlands and the Red Sea coast.