Stewart Stevenson has agreed council leaders to discuss the issue, which has sparked fury in the island communities.
Earlier, Shetland MSP Tavish Scott called for Mr Stevenson to resign after he announced a £6.5 m extension to the pilot road equivalent tariff scheme to the western isles.
The Lib Dems had accused the government of favouritism to the Western Isles. Mr Scott, a former transport minister himself, said the government was trying to rush through damaging cuts to create a "second rate service" without first assessing their impact or how much they would save.
Mr Stevenson told Mr Scott the information on the impact and potential saving flowing from each option was "currently being collated as part of the northern isles study process and will be made available in due course".
Mr Scott said: "This is further evidence that the government was so determined to cut support for NorthLink, very probably in order to help to pay for the cost of continuing their road equivalent tariff 'pilot' electoral bribe to the western isles, that they rushed ahead without even bothering to assess the impact of their proposals.
"NorthLink's traffic levels have grown since they took over the service. The income this produces helps to keep the overall support for the service down.