Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al Thani says that the four Arab countries had presented "claims that are not proved by evidence and are not demands."
Saudi Foreign Minister Adel bin Ahmed al Jubeir said on Tuesday that there would be no negotiations over the list of 13 demands by the kingdom and other Arab states for Qatar to stop supporting terrorism.
Doha retorted that the allegations against it and demands were baseless and unacceptable. Qatar has previously also said the demands were aimed at curbing its sovereignty.
Asked by reporters on a visit to Washington if the demands were non-negotiable, Saudi's Jubeir said, "Yes."
"We made our point, we took our steps and it's up to the Qataris to amend their behaviour and once they do, things will be worked out, but if they don't they will remain isolated," Jubeir said.
If Qatar wanted to return to the Gulf Cooperation Council fold, "they know what they have to do," he said.
Saudi FM: Our demands on Qatar are non-negotiable. It's now up to Qatar to end its support for extremism and terrorism. pic.twitter.com/vE1ovwAXcQ— (@KSAMOFA) June 27, 2017
Saudi Arabia, the United Arab Emirates, Bahrain and Egypt imposed a boycott on Qatar three weeks ago, accusing it of backing militants - then issued an ultimatum, including demands it shut down a Turkish military base in Doha, shutting down the Al Jazeera TV channel and curbing ties with Iran.
They closed their airspace to Qatari carriers and blocked the emirate's only land border, a vital route for its food imports. Doha meanwhile has gotten some lifeline support from Turkey, Iraq and Iran.
US Secretary of State Rex Tillerson met with Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al Thani at the State Department on Tuesday.
Al Jazeera quoted Thani as saying in response to Saudi's Jubeir that the countries had presented "claims that are not proved by evidence and are not demands."
"The demands must be realistic and enforceable and otherwise are unacceptable," Al Jazeera reported him as saying.
"We agree with Washington that the demands should be reasonable."
Last week United Arab Emirates' state minister for foreign affairs Anwar Gargash warned that Qatar should take the demands seriously or face "divorce" from its Gulf neighbours.
Tillerson has said he hopes the list of demands would be "reasonable and actionable."
On Sunday, Tillerson said that while some elements of the series of requests made by the four countries would be "very difficult for Qatar to meet," "there are significant areas which provide a basis for ongoing dialogue leading to resolution."
Asked about Jubeir's stance on Tuesday, Tillerson replied, "We hope all the parties will continue to talk to one another in good faith."
US State Department Spokeswoman Heather Nauert said on Tuesday that talks would continue through the week, but added the Saudi demands remained "challenging" for Qatar.
"Some of them will be difficult for Qatar to incorporate and to try to adhere to," she said.
"We continue to call on those countries to work together and work this out."
Tillerson followed the meeting with the Qatari foreign minister with a meeting with Kuwait Minister of State for Cabinet Affairs Sheikh Mohammad Abdullah al Sabah, whose country has taken on the official role of mediator in the crisis
The US Secretary of State also plans to meet in a working dinner late on Tuesday with the Kuwaitis and UN Secretary General Antonio Guterres, who has offered to help resolve the row as well.