The Scottish champions - one of the best supported clubs in Britain - went into administration on Tuesday after running into tax problems, leading to a 10-point penalty which has virtually gifted Celtic the title.
"On the issue of Rangers Football Club, this means a huge amount to many people in Scotland," United Kingdom Prime Minister David Cameron said in a statement on the club's website.
"I completely understand that no one wants to see, I certainly don't want to see Rangers Football Club disappear.
"There are discussions underway between [the tax authorities] and the administrator, I hope they can be successfully completed and I hope there will be a strong and successful future for Rangers."
Scotland's First Minister Alex Salmond said Rangers were an integral part of the country.
"We're talking about a huge institution, part of the fabric of the Scottish nation as well as Scottish football, and everyone realises that," Salmond said.
"The most diehard Celtic supporter understands that Celtic can't prosper unless Rangers are there. The rest of the clubs understand that as well."
But Celtic, who have dominated Scottish football with Rangers for over two decades, took issue with Salmond's comments.
"We are very disappointed with the First Minister's claims that Celtic 'need' Rangers and that Celtic can't prosper unless Rangers are there," Celtic said in a statement.
"This is simply not true. In a series of interviews given just three days ago, we made it abundantly clear that Celtic has a well-defined strategy and a business plan independent of the fortunes of any other club.
"The predicament of Rangers is clearly a serious and complex matter with a whole range of possible outcomes. However, we are extremely well qualified to make our own position clear and have no wish to see this being misrepresented for political reasons."
The lack of competition in the Scottish Premier League has long prompted calls for the Glasgow duo to join the richer English league but nothing has ever materialised, leaving Rangers and Celtic to lose out financially.
Administrators told a news conference that February wages will be paid and that there was no danger of liquidation at this stage, although further sales of the playing staff may occur.
Club chairman Craig Whyte told Sky Sports News he hoped Rangers would come out of administration next month.
Rangers could face a tax bill of 50 million pounds.
