Turkmenistan has insisted it cut gas to Iran 12 days ago because of a technical fault with the export pipeline and Iran's failure to pay for supplies.
The Turkmen foreign ministry said Tehran's failure to make the payments had been "holding back the completion of repair and maintenance work".
Iranian media reports earlier said Turkmenistan had wanted to double the price for the gas it exports to Iran.
The cut has been blamed for serious gas shortages in northern and western Iran.
Iranian President Mahmoud Ahmadinejad said on Friday that Turkmenistan had hampered his country's ability to cope with the recent severe cold and heavy snow that has caused at least 28 deaths, including eight from the cold.
In a statement, the Turkmen foreign ministry reiterated that natural gas shipments to Iran had been suspended since 1 January because of the need to perform repairs on the 200km (125 mile) export pipeline.
"Iran's failure to fulfil its obligations on payments for the previous natural gas shipments from Turkmenistan is holding back the completion of repair and maintenance work," it added.
Earlier on Sunday, the Iranian state-owned Press TV station had reported that one of the reasons for the cut was a dispute between the two countries on the price of gas.
It said Turkmenistan had proposed almost doubling the price agreed last year, from $75 (£38) per 1,000 cubic metres of gas to $140 (£71) per 1,000 cubic metres.
The Iranian Oil Minister, Gholamhossein Nozari, told the Fars news agency that Tehran would not discuss prices until Turkmenistan resumed its gas supplies.
Despite its massive oil and gas reserves, Iran imports about 5% of its natural gas supply from Turkmenistan.
In November, the Russian state-run gas firm, Gazprom, agreed to pay Turkmenistan up to 50% more for its gas, increasing the price from $100 (£48) per 1,000 cubic metres to $150 (£77).