The UN-brokered truce, which began in April and has been extended three times in two-month increments, will expire on October 2.
UN officials hope that this iteration of the truce will be expanded beyond two months.
In an interview with Al Jazeera on Monday, Mr Grundberg said he is waiting for the warring parties to respond to a UN proposal for expanding the truce.
“We are entering a sensitive period where we're only less than nine days away from the end of the month of October — we had provided to all parties a proposal for a longer truce and what we want is for them to have a full commitment to see this achievement through and to find a political track for a permanent solution,” Mr Grundberg said.
During the 77th UN General Assembly in New York last week, the head of Yemen's Presidential Leadership Council (PLC) Rashad Al Alimi voiced his support for keeping the truce in place as long as it is not used by the Houthis as a launch pad for more serious escalations.
“The PLC strongly welcomes renewing the truce as long as it does not come at the expense of the future of Yemen's people, while preparations for a bloodier stage ahead are under way and terrorist militias are empowered, threatening not only Yemen or the region but the entire world,” he said.
Mr Al Alimi also said that Houthi breaches of the truce had resulted in the deaths of 300 people in Yemen.
On Monday, Yemenis marked the 60th anniversary of the formation of the republic during the 1962 revolution.
The army held a military parade in the recently liberated governorate of Marib and Yemenis took to the streets, waving flags and shouting patriotic slogans.
People even gathered in the capital Sanaa, where the Houthis took control in a 2014 coup. They have since banned demonstrations and exercise stringent security controls over civilians.
“The right to peaceful assembly and demonstration is a human right guaranteed by law … However, today in Sanaa and on the occasion of September 26, the youth found an opportunity to go out to Al Sabeen Square and express their rejection of the Houthi project and celebrate,” activist Riyadh Aldubai wrote on Twitter.
Rasha Jarhum — founder and director of the Peace Track Initiative, which works closely with the UN — said the celebrations in Sanaa “show that the people are fed up with Houthi rule”.
“The government of Marib's military parade is another message to the Houthis that a military solution is ready.”