The government, which rejected two private sector-led bids for the bank, announced legislation allowing it to take over Britain's fifth-largest mortgage bank on Sunday.
It has consistently said the nationalisation, the first in Britain since engine-maker Rolls-Royce was brought under public ownership in 1971 by the then ruling Conservatives, would be only temporary.
But the government declined to comment on Monday on how long public ownership could last.
"We can't have a timetable when we're talking about the return of better market conditions as a first step," Brown said.
Both Brown and Alistair Darling, his finance minister, said the bank would be run at arms' length and on a commercial basis.
The government now faces the threat of a drawn-out legal battle with disgruntled shareholders.
Shareholders in Northern Rock reacted with anger as the suspension of the bank's shares left them unable to sell their stock.
The UK's Daily Telegraph newspaper quoted Jon Wood, founder of the bank's largest shareholder SRM Capital, as saying: "We will wait to see the details of the nationalisation bill and after that we will pursue all ... actions available to us to secure value for shareholders."
The UK shareholders' association said it would not accept a solution which could allow an eventual buyer to profit.
An independent audit is set to determine the value of the shares and how much the government will pay shareholders.
Opposition politicians blame Brown for the crisis, pointing to the regulatory framework he put in place a decade ago when he was finance minister under Tony Blair.
While the government has criticised Northern Rock's business model, Brown blames the bank's problems on a credit crisis that started with risky mortgage lending in the US and has since spread throughout the world's banking system.
Day-to-day running of Northern Rock will pass to Ron Sandler, who rescued Lloyd's of London from the brink of collapse.
Sandler visited the bank's headquarters in Newcastle on Monday.