Kuwait insisted it held "exclusive rights" to the maritime field along with Saudi Arabia, after the neighbouring countries agreed to jointly develop it last year.
The field, known as Arash in Iran and Dorra in Kuwait and Saudi Arabia, is also claimed by Tehran in a dispute which dates back several decades.
"The State of Kuwait and the Kingdom of Saudi Arabia... alone have exclusive rights to the natural wealth in the Al-Dorra field," a Kuwaiti foreign ministry statement said.
"The State of Kuwait renews its invitation to the Iranian side to start negotiations on the demarcation of the maritime borders," it added.
Last year, Kuwait and Saudi Arabia signed an agreement to develop the field, despite objections from Tehran which branded the deal as "illegal".
Mohsen Khojsteh Mehr, managing director of the National Iranian Oil Company, said last week that "there is full preparation to start drilling in the joint Arash oil field".
"Considerable resources have been allocated to the board of directors of the National Iranian Oil Company for the implementation of the development plan for this field," he said in remarks carried by Iranian state media.
His comments came as Saudi Arabia and Tehran boost cooperation after a shock decision to resume ties, announced in March, ended seven years of enmity between the major Gulf powers.
Kuwait's oil minister, Saad Al-Barrak, said he was "surprised" by the Iranian plans which he claimed "contravene the basic principles of international relations".
"We categorically and totally reject Iran's planned activities around the premises of the Dorra offshore gas field," Barrak added, according to official news agency KUNA.
The row over the Dorra field stretches back to the 1960s, when Iran and Kuwait each awarded an offshore concession, one to the Anglo-Iranian Oil Company, the forerunner to BP, and one to Royal Dutch Shell.
The two concessions overlapped in the northern part of the field, whose recoverable reserves are estimated at some 220 billion cubic metres (seven trillion cubic feet).
Iran and Kuwait have held unsuccessful talks for many years over their disputed maritime border area, which is rich in natural gas.
Saudi Arabia is also a part of the dispute since it shares with Kuwait maritime gas and oil resources in the area.
Iranian drilling of the field in 2001 spurred Kuwait and Saudi Arabia to agree on a maritime border deal which stipulated that they jointly develop the offshore zone.