Saudi Arabia and allies Egypt, Bahrain and the United Arab Emirates (UAE) severed ties with Qatar last week, accusing it of supporting Islamist militants and Iran - charges Doha denies.
The rift has disrupted travel, separated families, severed commercial links and sown confusion among banks and businesses.
"(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".
Morocco, a close ally of the Gulf countries, said on Sunday it would remain neutral and offered to facilitate dialogue.
"If the parties so wish, the Kingdom of Morocco is ready to offer its services to foster a frank and comprehensive dialogue on the basis of non-interference in internal affairs and the fight against religious extremism," a statement from the country's foreign ministry read.
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.
,(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 Foreign Minister Sheikh Sabah al-Khalid al-Sabah said
Qatar is ready to listen to the concerns of Gulf Arab states that have cut diplomatic and economic ties, Kuwait said on Sunday, as it tried to mediate a solution to the worst regional crisis in years.
