Tillerson has urged Arab states to "sit down together" to try to reach resolution while also noting that the list of demands on Qatar that have imposed a blockade against it "will be very hard to meet".
"It falls on us Europeans to convince the U.S. to continue supporting the worldwide system", Gabriel said at a speech given to the European Council on Foreign Relations.
Under US law, Congress must be formally notified 30 days before the sale of any weapons to foreign governments, giving lawmakers time to block it if they object. The move has left Qatar under a de facto blockade by its neighbors.
He urged the countries to sit together to stop terrorism and counter extremism.
"Demanding that Turkey pull its soldiers is unfortunately also disrespectful toward Turkey", he said.
While the Qatari Foreign Ministry has yet to issue an official reply, the director of the government's communications office, Sheikh Saif Al-Thani, called the Gulf States' demands "unrealistic" and said they were aimed at limiting Qatar's sovereignty.
Under American pressure, the bloc Friday issued a 13-demand list ordaining Qatar, among others, to reduce its diplomatic ties with its neighbor Iran and to expel members of Iran's Revolutionary Guards in Qatar.
While Tillerson, a former oilman who negotiated major deals in the region, has sought to calm the situation and work with all parties to the dispute, President Donald Trump has repeatedly sided with the Saudis.More news: Jordan Spieth goes full 'Happy Gilmore' in celebrating walk-off win
Opposition: Qatar hands over records/data on opposition they supported and kind of support they received.
The three Arab Gulf countries, along with Egypt, which also severed relations, have not provided any evidence for their claims, while Qatar has repeatedly denied the allegations as "baseless".
Qatar wants help from the U.S.in getting out from under sanctions.
Tillerson said Sunday that a number of the demands on Qatar would be "very hard to meet", and urged the United States allies to resolve their dispute.
The blockade of Qatar is "unacceptable" and Tehran's policy is to strengthen ties with Doha, Iran's state-run Islamic Republic News Agency cited President Hassan Rouhani as saying on Sunday.
According to Qatar News Agency reports, its #Human Rights Committee has condemned some of the requirements by the neighboring states, stating that they are not obtainable by worldwide human rights standards.
Qatar faces the prospect of diplomatic isolation in the long-term if it does not accept the demands made by its Gulf neighbours to end the ongoing dispute, a United Arab Emirates (UAE) minister warned on Saturday.
Tillerson said it would be better if the countries involved called for a meeting to iron out their differences.