"They will not have a positive impact on the region but a negative one", the minister said while on a visit to Germany.
Tillerson said that the GCC "must emerge united and stronger" to show its resolve.
"So far five planes carrying perishable food items such as fruit and vegetables have been sent to Qatar, each carrying around 90 tonnes of cargo, while another plane will be sent today", Iran Air spokesman Shahrokh Noushabadi said.
President Donald Trump has scrambled U.S. diplomacy on two fronts, delivering a rebuke of Qatar at the very moment his secretary of state was trying to mend fences in the Persian Gulf, while at the same time reaffirming support for North Atlantic Treaty Organisation two weeks after he had declined to do so.
Saudi Arabia said Sunday it was ordering "suitable measures" to help families with mixed citizenships but provided few details.More news: Man Utd Reportedly Agree Personal Terms With Zlatan Ibrahimovic Replacement
Indians, at 6,30,000, comprise the largest expatriate community in gas-rich Qatar which is by size a small nation.
"Qatar Petroleum.is conducting business as usual throughout all its upstream, midstream and downstream businesses and operations, and in all activities across all of QP's world-class facilities", a statement read.
Foreign Minister of Qatar Mohammed bin Abdulrahman bin Jassim Al Thani speaks with his Russian counterpart during their meeting in Moscow on June 10, 2017.
German Foreign Minister Sigmar Gabriel has warned that a row between Qatar and its Arab neighbors of the Persian Gulf region could end in a war.
It is unclear whether these deliveries are exports or aid.
He said the US supports the emir of Kuwait in his efforts to resolve the conflict and closed by calling upon the Gulf Cooperation Council - a regional political alliance between Oman, Bahrain, Kuwait, Qatar, Saudi Arabia and the UAE - to reaffirm the spirit of the summit attended by Trump three weeks ago, during which all of the countries committed to fight against terrorism.
With about 11,000 military personnel, Al Udeid Air Base is the largest US military installation in the Middle East and the forward headquarters of CENTCOM.
US Secretary of State Rex Tillerson shortly before Trump's remarks said the Gulf countries' land and air blockade of Doha was hurting the campaign against IS, an assessment Pentagon officials only partially corroborated.