Saudi Arabia and allies Egypt, Bahrain and the United Arab Emirates (UAE) severed ties with Qatar last week, accusing it of supporting terrorists and arch-foe Iran - charges Doha denies.
The rift has disrupted travel, separated families, severed commercial links and sown confusion among banks and businesses while deepening divisions between their respective allies fighting in wars and political struggles from Libya to Yemen.
"(Kuwait) affirms the readiness of the brothers in Qatar to understand the reality of the qualms and concerns of their brothers and to heed the noble endeavours to enhance security and stability," Kuwait's state news agency KUNA quoted Foreign Minister Sheikh Sabah al-Khalid al-Sabah as saying.
Kuwait, which has retained ties with Qatar and has often acted as a mediator in regional disputes, said it wanted to resolve the dispute "within the unified Gulf house".
A previous mediation effort by Kuwait in which the Emir Sheikh Sabah al-Ahmad al-Jaber al-Sabah shuttled between Riyadh, Abu Dhabi and Doha, failed to achieve an immediate breakthrough.
"Is this the beginning of wisdom and reasonable thinking? I hope so," UAE minister of state for foreign affairs Anwar Gargash wrote on Twitter in reaction to Kuwait saying Qatar was ready to listen to the grievances.
US President Donald Trump at first offered to host Qatar and its adversaries - all US allies - at the White House, but on Friday said Qatar has been a high-level sponsor of terrorism and backed the Gulf pressure.
Saudi Arabia's powerful Deputy Crown Prince Mohammed bin Salman discussed efforts to "counter terrorism and extremism" in a telephone call with US Secretary of State Rex Tillerson on Sunday, state news agency SPA said.
But a Qatari diplomat said the crisis reflected a lack of US leadership.
"This is the biggest testimony to US failure in the Gulf," the diplomat told Reuters, speaking on condition of anonymity. "(It) gives others the impression the US does not know how to manage the relationship with its allies or is incapable."
On Friday Saudi Arabia, Bahrain, the UAE and Egypt tightened their squeeze on Qatar by putting dozens of figures and charities they link to the country on terrorism blacklists.
Qatar's official overseer of charities denied on Sunday that philanthropic groups in the country backed terrorism, saying it deplored the accusation.
A peninsular nation of 2.5 million people, Qatar has for years punched well above its weight in world affairs by parleying its vast gas wealth into influence across the region, irking many with its maverick stances and support for Islamists.
But it was importing 80 percent of its food from bigger Gulf Arab neighbours before they cut ties and is now in talks with Iran and Turkey to secure food and water supplies.
Iran - the main regional rival of Saudi Arabia - sent four cargo planes of food to Qatar and plans to provide 100 tonnes of fruit and vegetables every day, Iranian officials said on Sunday, amid concerns of shortages.
Senior officials from the countries opposed to Qatar have warned it that appealing for foreign assistance will not advance a reconciliation.
Qatar's energy minister said on Sunday Doha remained committed to an oil output cut deal agreed by OPEC and non-OPEC producers last month.
Mohammed al-Sada said in a statement: "circumstances in the region shall not prevent the state of Qatar from honouring its international commitment of cutting its oil production".
In a sign Gulf states were seeking to lessen the human impact of their June 5 severing of ties, Saudi Arabia, Bahrain and the UAE said on Sunday they had set up hotlines to help families with Qatari members, without elaborating.
(Additional reporting by John Davison in Doha, Aziz El Yaakoubi in Dubai, Bozorgmehr Sharafedin in London, Katie Paul in Riyadh and Ahmed Hagagy in Kuwait; Writing by Sylvia Westall; Editing by Sami Aboudi and Mark Potter)