Theresa May chaired a meeting of the government's emergency committee on Monday morning to consider how to react to the capture of the Stena Impero on Friday.
Officials said the meeting would consider the options for "strengthening current reassurances" to commercial shipping as well as the response to Tehran.
The Prime Minister's official spokesman said: "We do not seek confrontation with Iran but it is unacceptable and highly escalatory to seize a ship going about legitimate business through internationally recognised shipping lanes."
Jon Heard from Apostleship of the Sea, a Christian charity providing welfare support to seafarers told Premier his concerns lie with the crew members: "It's important to remember these seafarers are just doing their jobs. They're working long contracts on these vessels, there's issues between Iran and Britain right now, but none of these seafarers are British nationals.
They're just innocent victims caught up in the middle.
Heard said it was important to consider both the crew members and their families, who face threat and disruption as a result of these political tensions, suggesting robust training was needed for other vessels to ensure seafarers are adequately equipped to enter the Persian Gulf.
He continued: "We know that seafarers themselves are finding this very stressful. It affects all seafarers travelling through the region and it's creating great stress and anxiety to all.
"It has a huge impact on their well-being and mental health, being at that high level of stress for so long.
"That's why we do what we can, working with the shipping companies, insurers and the port authorities to make sure that there is an independent voice; one of our chaplains, waiting at a port."
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.