A United Nations-brokered two-month nationwide cease-fire in Yemen that began Saturday has led to a "significant reduction in violence," said UN Special Envoy Hans Grundberg in a virtual press conference Wednesday.

"However," the Swede said, "there are reports of some hostile military activities, particularly around Marib, which are of concern," adding that the truce represented "both a precious and precarious moment."

"I would like to reiterate that this truce is a step, an important one, but a fragile step, nonetheless. We need to make the best possible use of the window this truce gives us to work towards ending the conflict," said Grundberg of the deal between the Saudi-backed Yemeni government and Iran-backed Houthi rebels.

Rebels have sought to wrest the energy-rich province of Marib from government forces for more than a year but have been thwarted by increased Saudi support for the government in Sanaa.

UN hopes cease-fire will allow parties to come to a political solution

Grundberg told reporters that the agreement is not being monitored by the UN but said responsibility for upholding it lies, "squarely with the parties themselves." The UN is, however, working on creating mechanisms to ensure the two-month deal holds, giving all involved the chance to come to a political solution to a conflict that has raged for years.

The cease-fire allows for fuel arrivals at the port of Hodeida and passenger flights in and out of Sanaa, both of which are under rebel control. Fuel shortages have sent prices skyrocketing and forced the closure of hospitals in recent months.

Grundberg said he had also invited both parties for talks on opening roads to provinces such as Taiz, which has been sealed off by the Houthis for years.

Now predominantly a proxy war between Riyadh and Tehran, the conflict began when Houthi rebels seized the capital Sanaa in September 2014. A Saudi-led coalition joined the effort to restore Yemen's government in March 2015.

Since then, more than 150,000 people — over 14,000 of whom were civilians — have been killed. Millions more have been displaced and face starvation in what has become one of the worst humanitarian catastrophes on the planet.