The company has "paused" production at its Redcar blast furnace blaming a slump in demand and rising costs.
SSI took over the former Tata Steel complex after it was mothballed in 2010 and employs almost 2,000 people.
Ms Soubry said EU rules meant state cash could not be directly used to support British steel production.
SSI chief operating officer Cornelius Louwrens called on the government to "take action rather than use just words" to help ensure the plant survives.
He said: "Other European countries are finding ways to support their steel industries because they believe it is so important."
He urged ministers to approve the underwriting of "key projects" to enable it to secure commercial loans, as well as reduce business rates and ease restrictions linked to CO2 emissions.
But, Ms Soubry said: "There are extremely strict state aid rules, which especially apply to the steel industry, so we are limited as to what we can do.
"We can put money into things like research and development. But simply giving a loan or underwriting things, we cannot do.
"Things are extremely difficult at SSI, but our hands are tied. However, we will continue to work with the company and the trade unions, but the underlying problem in all of this is that there is an overproduction of steel across the world.
"The prime minister has said that this is a vital British industry and government will continue to do all it can to help and assist it."
Unions at the plant have described the company's decision as "devastating" and have sought urgent talks with management.
The UK government is "limited" in what it can do to aid ailing Teesside steel firm SSI because of strict EU rules, business Minister Anna Soubry has said.