text: However, Mr Tillerson said the proposals provided a basis for dialogue leading to a solution of the crisis.
  On Saturday, Qatar's foreign minister rejected the list of 13 conditions imposed by Saudi Arabia and its allies, Egypt, the UAE and Bahrain.
  They accuse Qatar of backing terrorism - a charge it denies.
  Qatar has been under unprecedented diplomatic and economic sanctions for more than two weeks, with Iran and Turkey increasingly supplying it with food and other goods.
  The four countries also want Qatar to reduce its ties with Iran and close a Turkish military base, setting a deadline on Friday of 10 days.
  Among other things, the fellow Gulf states have demanded the closure of Al Jazeera TV, which is funded by the Qatari government.
  Mr Tillerson said Qatar was assessing the demands and stressed there were "significant areas which provide a basis for ongoing dialogue leading to resolution".
  He urged the countries to sit together to stop terrorism and counter extremism.
  "A lowering of rhetoric would also help ease the tension," Mr Tillerson said.
  After the demands were made on Friday, White House spokesman Sean Spicer said the dispute was "a family issue" that the countries should work out together.
  On Saturday, Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani, quoted by Al Jazeera, said: "The US secretary of state recently called upon the blockading nations to produce a list of grievances that was 'reasonable and actionable'.
  "The British foreign secretary asked that the demands be 'measured and realistic.' This list does not satisfy that [sic] criteria."
  He said the demands were proof that the sanctions had "nothing to do with combating terrorism... [but] limiting Qatar's sovereignty, and outsourcing our foreign policy".
  Al Jazeera accused them of trying to silence freedom of expression, adding: "We assert our right to practise our journalism professionally without bowing to pressure from any government or authority."
  Qatar's main import routes - by land from Saudi Arabia and by sea from container ships docked in the UAE - have been disrupted, and much of the surrounding airspace has been closed to its air traffic.
  However, the small but wealthy country has so far avoided economic collapse by finding alternative routes.
  Qatari citizens living in neighbouring countries or with family living there have been hit harder, Reuters news agency notes, because of ultimatums issued for them to leave.
  The United Arab Emirates has been trying to mediate in the crisis.
  UAE's foreign minister said on Saturday there would be a "parting of ways" with Qatar if it failed to meet the demands.
  "The alternative is not escalation," he said. "The alternative is parting of ways. It's very difficult for us to maintain a collective grouping with one of the partners... actively promoting what is an extremist and terrorist agenda."
  US President Donald Trump has taken a hard line towards Qatar, accusing it of being a "high-level" sponsor of terrorism.
  However, the Arab states involved in the crisis are all close allies of the US, while the largest US base in the Middle East is in Qatar.
target: Some demands set by four Arab states on Qatar in return for lifting sanctions will be "difficult to meet", US Secretary of State Rex Tillerson says.