The Houthi delegation, which was due to arrive on Sunday, was still in Djibouti in east Africa on Monday evening.
Mr Ban warned that "while the parties bicker, Yemen burns" and urged an immediate humanitarian ceasefire.
An estimated 20 million Yemenis are in need of aid following months of fighting in the country.
The humanitarian situation has been described as "catastrophic" by the UN, with more than 2,000 people killed in the conflict.
Opening the talks, Mr Ban said: "Today Yemen's very existence hangs in the balance."
He urged action on three main areas: "First, a renewed humanitarian pause to allow critical assistance to reach all Yemenis in need and provide a respite for Yemenis as the holy month of Ramadan begins.
"Second, I urge the parties to reach agreement on local ceasefires. Third, I call on them to resume a peaceful and orderly political transition and to ensure that the process includes more representation from other political parties, women, youth and civil society."
The BBC's Imogen Foulkes in Geneva said the Houthi representatives were apparently delayed over what airspace their plane could fly through. She said that the confusion did not bode well for the talks.
A Saudi-led coalition of Arab states has been bombing the Houthi rebels and their allies since March.
The bombing campaign was launched to support Yemeni President Abdrabbuh Mansour Hadi, who escaped to the Saudi capital, Riyadh, when the Houthis advanced on his stronghold in Aden in southern Yemen.
In recent weeks, fighting between Saudi forces and the Houthis has intensified on Yemen's border with Saudi Arabia.
On Saturday, Saudi Arabia claimed to have shot down a Scud missile fired by the Houthis.
The attack followed fighting on the border on Friday, in which four Saudi soldiers and a number of Yemeni rebels died.
On the same day, bombs hit the Old City of Yemen's capital, Sanaa, killing five people according to local sources.

Jones, who led by three strokes heading into Sunday, dropped three shots in his first two holes and triple-bogeyed the ninth but rallied to end eight under.
American Spieth, who missed an eagle putt on the last to force a play-off, carded a 71 to finish joint second.
He was joined on seven under by Scott, who shot a superb six-under 65.
The round of the day, though, came from another Australian, Rod Pampling, who made a 60-foot eagle putt on the 18th green for a course record 10-under 61 to earn him a fourth-place finish on six-under.
This bettered the 63 Spieth carded in the final round to win the title last year.
Despite the leader's poor start and two birdies of his own on the front nine, 22-year-old Spieth was unable to capitalise before Jones' two birdies on the back nine gave him the win.
"That was very stressful, it wasn't comfortable out there for me," said Jones, whose victory earns him a place in next July's Open Championship at Royal Troon.
"I've watched the Australian Open for many years and just to have my name on that trophy is something I'll never forget."
Joining Jones at next year's 145th British Open Championship will be fellow  Australians Pampling and Nick Cullen.
Cullen shot a 68 in his final round to share fifth place and earn the third qualifying place.
England's Lee Westwood carded his best round of the tournament - a two-under 69 - to finish tied for 18th on two under, while a 76 from Northern Ireland's Darren Clarke left him joint 30th on four over.
UN Secretary General Ban Ki-moon has opened talks in Geneva on the conflict in Yemen but without the presence of Houthi rebel representatives.
[NEXT_CONCEPT]
Matt Jones held off a challenge from world number one Jordan Spieth and fellow Australian Adam Scott to win the Australian Open by a shot.