"We have made a decision to continue talks until Saturday," Yassin told reporters.
The UN-brokered session kicked off on Monday without the Shiite Houthi movement's participation, and was initially expected to wrap up on Wednesday.
The Houthis, whose positions have been subject to Saudi-led coalition airstrikes since late March, were held up in Djibouti in what they described as Riyadh's attempt to torpedo negotiations.
Their delegation eventually arrived in Geneva on Tuesday.
Yemen has been in a state of political and military turmoil since late 2014, when the country's leading rebel group at the time began seizing territory, culminating in the capture of the capital of Sanaa in January.
The death toll from the Arab coalition's air campaign in the country has led to 1,412 civilian deaths, the UN humanitarian office announced on Tuesday. UN spokesman Stephane Dujarric said last week an estimated 80 percent of Yemen's population, over 21 million, is in need of humanitarian assistance.
UN Secretary-General Ban Ki-moon called for a two-month ceasefire on the first day of the Yemeni peace talks to mark the month of Ramadan, observed from June 18 to July 16.
