The United States has called on Arab states to ease their blockade on Qatar and demanded all sides move to calm tensions that intensified with a Turkish offer to send troops, warships and planes to aid its Qatari ally.

Saudi Arabia, the United Arab Emirates (UAE), Egypt and Bahrain, which on Monday cut ties with Qatar and accused it of fomenting instability, tightened their squeeze by putting dozens of figures with links to the tiny, wealthy nation on terrorism blacklists.

In something of a reversal of U.S. President Donald Trump's suggestion earlier this week that he sided with Saudi Arabia and other countries against Qatar, U.S. Secretary of State Rex Tillerson made clear on Friday that he expected all parties to end the crisis.

"We call on the kingdom of Saudi Arabia, the United Arab Emirates, Bahrain and Egypt to ease the blockade against Qatar," he said in Washington.

Tillerson told reporters at the State Department that the crisis, which has cut transportation links and trade, had begun to hurt ordinary people in Qatar, impaired business dealings and harmed the U.S. battle against the Islamic State militant group.

He demanded that Qatar, as well as the other nations, take steps to curtail support for terrorism. Saudi Arabia and other Gulf states accuse Doha of supporting extremist groups, but Tillerson suggested that all sides needed to do more.

"The emir of Qatar has made progress in halting financial support and expelling terrorist elements from his country, but he must do more and he must do it more quickly," Tillerson said. "Others must also continue to eliminate factions of support for violent organisations within their own borders."

Al Jazeera said its computer systems had come under attack. Photo: Reuters

In an apparent escalation of the crisis, staff at Al Jazeera, Qatar's influential satellite television news channel which often infuriates the rulers of the Arab world, said its computer systems had come under cyber attack.

Riyadh, Cairo and their allies accuse Qatar, the world's richest country per capita, of supporting militant Islamist movements across the region. They have imposed what Qatar says is a blockade of shipping and air traffic and closed Qatar's only land border, causing panic buying at supermarkets and provoking confusion and anxiety across the population.

Qatar, which has developed an assertive foreign policy over the past decade, denies that it supports militants and says it is helping to reduce the threat of terrorism by backing groups that fight poverty and seek political reform.

Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani called the moves by Arab neighbours and others "clear violations of international law and international humanitarian law.

"They will not have a positive impact on the region but a negative one," the minister said during a visit to Germany.

Qatar has vowed to ride out the isolation imposed on it by fellow Arab states and said it would not compromise its sovereignty over foreign policy to resolve the region's biggest diplomatic crisis in years.